## سوالات GRE Power Prep Plus به همراه پاسخنامه

GRE Power Prep Plus with answers

## PPS1-Set1

PPS1-Set1
1.
n > 1

125n

#### Quantity B

215(n-1)

• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
2. Quantity A:The area of an isosceles triangle that has one right angle and two sides of length 2

Quantity B:The area of an equilateral triangle that has sides of length 2
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
3.

Quantity A:x

Quantity B:y
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
4. Quantity A:The number of integers from 1 to 300 that are divisible by both 5 and 9

Quantity B:6
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
5. A car travels d miles along a stretch of highway at a constant speed of r miles per hour and then travels d miles back to its starting point at a constant speed of s miles per hour, where r > s .

Quantity A:The time taken by the car to travel the d miles at r miles per hour

Quantity B:$$\frac{d}{s}$$ hours
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
6. -10< x+y< 20

5< x< 10

Quantity A:y

Quantity B:-15
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
7. R=$$(2^{16})(5^{34})(N^{50})$$,where N is a positive integer.

Quantity A:$$\sqrt{R}$$

Quantity B:$$\frac{R}{10}$$
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
8. 2s=r+t

Quantity A:The median of r, s, and t

Quantity B:s
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set1
9. A copy machine was used to produce two smaller versions of a rectangular picture. Each dimension of the original picture was reduced by 20 percent to produce the first smaller version, and then each dimension of the first smaller version was reduced by 15 percent to produce the second smaller version. Each dimension of the second smaller version was what percent of the corresponding dimension of the original picture?
• A . 35%
• B . 38%
• C . 65%
• D . 68%
• E . 70%
PPS1-Set1
10. A metal right circular cylinder is 20 centimeters tall, has a base with diameter 8 centimeters, and is open at both ends. Which of the following is closest to the outside surface area of the cylinder, in square centimeters?
• A . 450
• B . 475
• C . 500
• D . 525
• E . 550
PPS1-Set1
11.

Matt has 10 coins, and their values are shown in the table. If Matt randomly selects 4 of the coins, which of the following could be the total value of the 4 coins?

Indicate all such values.
• A . $0.25 • B .$0.26
• C . $0.27 • D .$0.28
PPS1-Set1
12. If$$\frac{x+1}{6x}+\frac{x+1}{2x}=1$$ , what is the value of x ?

x=_____
PPS1-Set1
13. x,12,11

If the standard deviation of the three numbers in the list above is 4, what is the standard deviation of x+9, 21, and 20 ?
• A . 4
• B . 13
• C . 31
• D . 36
• E . 108
PPS1-Set1
14.

According to a projection made in January 2016, for each of the three years following 2015, annual sales would increase by an amount equal to $$\frac{1}{2}$$ of the increase in annual sales from 2014 to 2015. According to this projection, approximately what would annual sales be for the year 2018 ?
• A . $2,200 million • B .$2,425 million
• C . $3,450 million • D .$4,050 million
• E . $4,875 million PPS1-Set1 15. • A . For the years shown, the range of the annual earnings was greater than$30 million.
• B . From 2010 to 2015, both annual sales and annual earnings more than doubled.
• C . For each of the years shown, annual earnings were more than 1 percent of annual sales.
PPS1-Set1
16.

The number of stores owned by Star Discount in 2015 was twice the number owned by Star Discount in 2010. By approximately what percent did the average annual earnings per store increase from 2010 to 2015 ?
• A . 5%
• B . 12%
• C . 25%
• D . 33%
• E . 40%
PPS1-Set1
17. In a certain list of positive integers, the ratio of the number of odd integers to the number of even integers is 7 to 4. One-fourth of the number of odd integers is what fraction of the total number of integers in the list?
• A . $$\frac{7}{44}$$
• B . $$\frac{3}{16}$$
• C . $$\frac{11}{28}$$
• D . $$\frac{7}{16}$$
• E . $$\frac{9}{16}$$
PPS1-Set1
18. If the circumference of a circle is 6, what is the area of the circle?
• A . $$\frac{6}{π^{2}}$$
• B . $$\frac{9}{π}$$
• C . 6π
• D . 9π
• E . 36π
PPS1-Set1
19. In the xy-plane, the graph of the equation y=$$-\frac{1}{2}x+3$$ passes through the point (c,-c). What is the value of c ?
• A . -6
• B . -3
• C . 2
• D . 3
• E . 6
PPS1-Set1
20. On a final exam, 75 percent of a class had scores that were greater than 70, and 60 percent of the class had scores that were less than 85. What percent of the class had scores that were greater than 70 but less than 85 ?

_____%

## PPS1-Set2

PPS1-Set2
1.

The area of the shaded region inside rectangle RSTW is 28.

Quantity A:The sum of the areas of the unshaded regions inside rectangle RSTW

Quantity B:42
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
2. List K consists of 10 numbers whose standard deviation is 7.

List M is formed by adding 3 to each number in list K.

Quantity A:The standard deviation of the numbers in list M

Quantity B:7
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
3.
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
4. At a community college, 36 students are enrolled in a psychology class and 28 students are enrolled in a statistics class. Of the students enrolled in the psychology class, 17 are also enrolled in the statistics class.

Quantity A:The number of students at the college who are enrolled in only one of the two classes

Quantity B:30
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
5. x<8

Quantity A:|x|

Quantity B:9
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
6.

Quantity A:x

Quantity B:y
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
7. 0 < p < 1

n is a positive integer.

Quantity A:$$p^{n}$$

Quantity B:$$p^{-n}$$
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set2
8.

According to the graph, the kiosks of which of the following two types combined account for $$\frac{6}{25}$$ of all the kiosks?
• A . Entertainment and retail
• B . Entertainment and financial services
• C . Entertainment and travel/tourism
• D . Communications and government
• E . Retail and financial services
PPS1-Set2
9. 0.4, 0.8, 1.2, 2.0, y

If the average (arithmetic mean) of the 5 numbers in the list above is 1.0, what is the value of y ?
• A . 0.2
• B . 0.4
• C . 0.6
• D . 0.8
• E . 1.0
PPS1-Set2
10. In a certain sequence of numbers, each term after the first term is found by multiplying the preceding term by 3 and then subtracting 2 from the product. If the third term of the sequence is 55, what is the first term of the sequence?
• A . 5
• B . 6
• C . 7
• D . 8
• E . 9
PPS1-Set2
11. Points P, Q, and R lie on a line, and point Q is between point P and point R. The length of line segment PQ is 5. Which of the following could be the length of line segment PR ?

Indicate all such lengths.
• A . 2
• B . 4
• C . 6
• D . 8
PPS1-Set2
12. If c, d, and e are integers greater than 1 and cde=66, what is the value of c+d+e ?
• A . 16
• B . 19
• C . 20
• D . 33
• E . 35
PPS1-Set2
13. An initial amount of 600 grams of a saltwater solution that was 5 percent salt, by mass, was reduced to 300 grams of solution by evaporating some of the water. If the amount of salt remained the same, then the resulting solution was what percent salt?
• A . 60%
• B . 30%
• C . 20%
• D . 10%
• E . 6%
PPS1-Set2
14.

Notes:

(1) The total population was 260,341,000.

(2) Age-group determined by age, in years, at last birthday.
Approximately how many people were age 24 years or younger?
• A . 25 million
• B . 36 million
• C . 68 million
• D . 87 million
• E . 93 million
PPS1-Set2
15.

Notes:

(1) The total population was 260,341,000.

(2) Age-group determined by age, in years, at last birthday.
The median age of the population is in which of the four age-groups shown?
• A . 17 and younger
• B . 18 to 24
• C . 25 to 44
• D . 45 and older
• E . It cannot be determined from the information given.
PPS1-Set2
16.

Notes:

(1) The total population was 260,341,000.

(2) Age-group determined by age, in years, at last birthday.
Which of the following information, if any, together with the information given, is sufficient to determine the average (arithmetic mean) age for the population?
• A . The number of people in each age-group
• B . The average age for each age-group
• C . The median age for each age-group
• D . The median age for the population
• E . No additional information is needed; the information given is sufficient.
PPS1-Set2
17. John and Paul begin work at 8:00 in the morning and finish at 4:30 in the afternoon. John begins his first break of the day at 8:45 and his second break at 9:30, and he continues to take a break every 45 minutes throughout the day. Paul begins his first break at 9:00 and his second break at 10:00, and he continues to take a break every 60 minutes throughout the day. At which of the following times do John and Paul begin a break at the same time?

Indicate all such times.
• A . 10:00 in the morning
• B . 11:00 in the morning
• C . 12:00 noon
• D . 1:00 in the afternoon
• E . 2:00 in the afternoon
• F . 3:00 in the afternoon
• G . 4:00 in the afternoon
PPS1-Set2
18. In the xy-plane, a quadrilateral has vertices at (-9,-2), (-1,-2) ,(-1,-4) , and (-9,-4). What is the perimeter of the quadrilateral?
• A . 4
• B . 10
• C . 20
• D . 24
• E . 32
PPS1-Set2
19. The total charge for a 4-week dance class is $55.00. The class has 3 sessions per week, and each session lasts 45 minutes. Approximately what is the charge per hour for the class? • A .$18.30
• B . $13.75 • C .$6.10
• D . $5.35 • E .$4.60
PPS1-Set2
20. If$$4^{x}=256$$ , what is the value of $$2^{2x-1}$$ ?

$$2^{2x-1}$$ =_____

## PPS1-Set3

PPS1-Set3
1. S={2,7,9,10,11,15}

A number r is to be selected at random from set S. Quantity A:The probability that the value of $$(-1)^{r^{2}}$$ will be 1 Quantity B:$$\frac{1}{2}$$
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
2. $$\frac{y}{8}=\frac{z}{16}$$

Quantity A:$$\frac{y+1}{4}$$

Quantity B:$$\frac{z+1}{8}$$
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
3. Quantity A:$$\frac{2}{\sqrt[3]{6}}+\frac{3}{\sqrt[3]{6}}$$

Quantity B:$$\frac{\sqrt[3]{6}}{2}+\frac{\sqrt[3]{6}}{3}$$
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
4. The length of each side of square PQRS is greater than 3. The radius of circle C is 3.

Quantity A:The area of square PQRS

Quantity B:The area of circle C
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
5.

The ratio of PW to PR in rectangle PRSW is equal to the ratio of PQ to QT in rectangle PQTW.

Quantity A:x

Quantity B:20
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
6. For 1 year, Maria invested $10,000 at a simple annual interest rate of x percent and$8,000 at a simple annual interest rate of y percent, where$$x=\frac{3y}{4}$$and y>0.

Quantity A:The amount of interest earned on the $10,000 investment Quantity B:The amount of interest earned on the$8,000 investment
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
7. The points (r,s) and (t,u) are in the xy-plane, where r, s, t, and u are all less than 0 and r≠t.

Quantity A:The slope of the line that passes through (r,s) and (t,u)

Quantity B:0
• A . Quantity A is greater.
• B . Quantity B is greater.
• C . The two quantities are equal.
• D . The relationship cannot be determined from the information given.
PPS1-Set3
8. 14.6, 12.6, 16.3, 16.2, 16.2, 17.8, 17.7, 16.0, 14.6, 12.6

The readings of the electric meter for a certain business for each of 10 months are listed above. What is the median of the readings?
• A . 16.0
• B . 16.1
• C . 16.2
• D . 16.25
• E . 16.3
PPS1-Set3
9. When measured from sea level, the height of Mountain C is 40 percent of the height of Mountain D. If the height of Mountain C is greater than 800 meters, which of the following values could be the height, in meters, of Mountain D ?

Indicate all such values.
• A . 1,200
• B . 1,500
• C . 1,600
• D . 1,800
• E . 2,500
• F . 3,000
PPS1-Set3
10. An empty box weighs 50 ounces. The box is to be packed with at least 98 units of a certain product but not more than 102 units. If each unit weighs 0.82 ounce and the packed box weighs w ounces, then w must satisfy which of the following inequalities?
• A . 80.36≤w≤83.64
• B . 88.56≤w≤112.2
• C . 119.50≤w≤132.64
• D . 130.36≤w≤133.64
• E . 131.55≤w≤137.56
PPS1-Set3
11. The integers s and t are divisible by 5. Which of the following is NOT necessarily true?
• A . s-t is divisible by 5.
• B . s+t is divisible by 10.
• C . st is divisible by 25.
• D . $$s^{2}-t^{2}$$ is divisible by 5.
• E . $$s^{2}+t^{2}$$ is divisible by 25.
PPS1-Set3
12.

The figure shows some of the dimensions, in meters, of a building with eight sides. The perimeters of rectangular regions X, Y, and Z are 28, 34, and 22 meters, respectively. What is the perimeter of the building, in meters?
• A . 60
• B . 64
• C . 70
• D . 74
• E . 84
PPS1-Set3
13. If x=3 is a solution of the equation $$x^{2}+bx-18=0, where b is a constant, then the other solution is • A . x=15 • B . x=9 • C . x=6 • D . x=-3 • E . x=-6 PPS1-Set3 14. For 2008 the annual earnings of the European division were approximately what percent of the combined annual earnings of the two divisions? • A . 25% • B . 40% • C . 50% • D . 60% • E . 75% PPS1-Set3 15. If the annual earnings of the European division for 2009 represented 7 percent of the divisions annual revenues, approximately how much were its annual revenues? • A . 11 billion • B . 21 billion • C . 37 billion • D . 105 billion • E . 214 billion PPS1-Set3 16. For the years shown, the range of the annual earnings of the United States division was approximately how much greater than the range of the annual earnings of the European division? • A . 1.5 billion • B . 2.7 billion • C . 3.6 billion • D . 4.3 billion • E . 5.0 billion PPS1-Set3 17. The average (arithmetic mean) of w, x, y, and z is equal to the average of x, y, and z. Which of the following expressions represents w in terms of x, y, and z ? • A .$$\frac{x+y+z}{4}$$• B .$$\frac{x+y+z}{3}$$• C .$$\frac{3(x+y+z)}{4}$$• D .$$\frac{4(x+y+z)}{3}$$• E . 12(x+y+z) PPS1-Set3 18. How many integers between 115 and 969 are cubes of integers? _____ PPS1-Set3 19. The width of rectangle T is 25 percent greater than the width of rectangle R, and the length of T is 10 percent greater than the length of R. The area of T is what percent greater than the area of R ? • A . 2.5% • B . 15% • C . 27.3% • D . 35% • E . 37.5% PPS1-Set3 20. If -1 < x < 1 and x≠0, which of the following statements must be true? Indicate all such statements. • A . x<$$\frac{1}{x}$$• B .$$x^{2}$$< x • C .$$ x^{3} < x^{2}$$Download PPS1-Set3 Quant Answers ## PPS1-Set4 PPS1-Set4 1. Each of the 120 people in a group donated one of three different amounts to charity. Of the people in the group,$$\frac{2}{3}$$donated 10.00 each,$$\frac{1}{4}$$donated 15.00 each, and the rest donated 25.00 each. Quantity A:The average (arithmetic mean) amount donated per person in the group Quantity B:12.50 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 2. -|x|=|x| Quantity A:x Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 3. Quantity A:The greatest possible value of$$\frac{2}{x-y}$$, where 6≤x≤8 and 2≤y≤5 Quantity B:$$\frac{2}{3}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 4. The function f is defined by$$f_{(x)}=x(x^{2}-4)$$for all numbers x. Quantity A:The number of points at which the graph of$$y=f_{(x)}$$intersects the x-axis in the xy-plane Quantity B:3 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 5. 0 < r < v < x < y < z Quantity A:The average (arithmetic mean) of the 4 numbers r, v, y, and z Quantity B:The average (arithmetic mean) of the 5 numbers r, v, x, y, and z • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 6. The volume of a right circular cylinder is 2,000π, and its height is 16 times its radius. Quantity A:The radius of the cylinder Quantity B:5 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 7.$$C_{1},C_{2},C_{3},...C_{j}...$$The sequence shown is defined by$$C_{1}=5$$and$$C_{j+1}=\frac{1}{5}C_{j}$$for each positive integer j. Quantity A:$$C_{10}$$Quantity B:$$5^{15}C_{25}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS1-Set4 8. An investor placed a total of 6,400 in two accounts for one year. One of the accounts earned simple annual interest at a rate of 5 percent, and the other earned simple annual interest at a rate of 3 percent. The investor made no deposits or withdrawals from the accounts. If each account earned the same amount of interest after one year, what was the total amount of interest earned from both accounts? • A . 128 • B . 144 • C . 240 • D . 256 • E . 512 PPS1-Set4 9. A flat rectangular tile has a length that is between 4 inches and 6 inches and a width that is between 3 inches and 6 inches. Which of the following could be the value of the area, in square feet, of the top surface of the tile? (1 foot = 12 inches) Indicate all such values. • A .$$\frac{1}{8}$$• B .$$\frac{1}{6}$$• C .$$\frac{1}{2}$$• D .$$\frac{4}{3}$$PPS1-Set4 10. If 2, 4, 6, and 9 are the digits of two 2-digit integers, what is the least possible positive difference between the integers? • A . 28 • B . 27 • C . 17 • D . 13 • E . 9 PPS1-Set4 11. In the figure, all intersecting line segments meet at right angles. Which of the following represents the perimeter of the figure in terms of x ? • A . 3x+15 • B . 4x+9 • C . 5x+19 • D . 6x+16 • E . 8x+18 PPS1-Set4 12. A certain experiment has only three possible outcomes. The probabilities of the outcomes are p, r, and s. If r=1-3p, what is s in terms of p ? • A . p • B . 2p • C . 3p • D . 1-p • E . 1-2p PPS1-Set4 13. When the positive integer d is divided by 12, the remainder is 5. What is the remainder when$$d^{2}$$is divided by 8 ? • A . 1 • B . 3 • C . 5 • D . 6 • E . 7 PPS1-Set4 14. Total number of commuters in Country S in June 2016: 8 million If 75 percent of the commuters were local commuters and if 20 percent of the local commuters used buses as their primary mode of transportation, what percent of all commuters who used buses as their primary mode of transportation were local commuters? • A . 6% • B . 15% • C . 30% • D . 60% • E . 75% PPS1-Set4 15. Total number of commuters in Country S in June 2016: 8 million For commuters who used car pools as their primary mode of transportation, the average (arithmetic mean) number of commuters per car pool vehicle was 2.5. Which of the following is closest to the total number of car pool vehicles for these commuters? • A . 0.02 million • B . 0.13 million • C . 0.32 million • D . 0.80 million • E . 1.20 million PPS1-Set4 16. Total number of commuters in Country S in June 2016: 8 million From June 2016 to December 2016, the total number of commuters increased by x percent while the percent of commuters who used trains as their primary mode of transportation remained the same. If the number of commuters who used trains as their primary mode of transportation increased by 16,000 from June to December, what is the value of x ? • A . 1 • B . 2 • C . 3 • D . 4 • E . 5 PPS1-Set4 17. The sale price of a certain radio is 25 percent less than the list price and 40 percent greater than the wholesale price of the radio. If the wholesale price of the radio is 30, what is the list price of the radio? • A . 52 • B . 53 • C . 54 • D . 55 • E . 56 PPS1-Set4 18. A list consists of three different positive integers whose sum is 10. Which of the following statements individually provide(s) sufficient additional information to determine the value of the greatest integer in the list? Indicate all such statements. • A . The median of the integers in the list is 3. • B . The range of the integers in the list is 5. • C . The sum of the greatest integer and the least integer in the list is 7. PPS1-Set4 19. A group of n college students bought three identical round cakes to share. They divided the first cake into equal-sized pieces, one piece for each of them. They did the same with the second cake. After 3 of the students decided they did not want any more cake, the remaining students divided the third cake into equal-sized pieces, one piece for each of them. If Silvia received 1 piece from each of the three cakes, then, in terms of n, the amount of cake that she received was the same as what fraction of 1 cake? • A .$$\frac{n+2}{n(n-3)}$$• B .$$\frac{2n-3}{n(n-3)}$$• C .$$\frac{3n-3}{n(n-3)}$$• D .$$\frac{3n-6}{n(n-3)}$$• E .$$\frac{3n-3}{2n(n-3)}$$PPS1-Set4 20. In the figure, lines k, l, and m intersect at a single point, which is the vertex of all the angles shown. If x=z, y=2w, and v=110 , what is the ratio of x to w ? Give your answer as a fraction. Download PPS1-Set4 Quant Answers ## PPS2-Set1 PPS2-Set1 1. 0< x< y< 1 #### Quantity A y-x #### Quantity B$$(x-y)^{2}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 2. Quantity A:N Quantity B:$$\frac{1}{2}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 3. Last Monday, James paid 8.00 per share for 180 shares of Stock X, paid 10.00 per share for 160 shares of Stock Y, paid 12.00 per share for 200 shares of Stock Z, and bought no other shares of stock. Quantity A:The average (arithmetic mean) price per share that James paid for all of the shares of stock he bought last Monday Quantity B:10.00 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 4. 2x+cy=10 6x+2cy=40 The system of equations shown has a solution, where c is a constant.Quantity A:c Quantity B:1 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 5. The average (arithmetic mean) of the 6 numbers q, r, s, t, u, and v is 36. Quantity A:$$\frac{q}{6}+\frac{r}{6}+\frac{s}{6}+\frac{t}{6}+\frac{u}{6}+\frac{v}{6}$$Quantity B:6 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 6. Quantity A:x+y+z Quantity B:360 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 7. In the figure shown, two rectangular regions overlap to form a triangular region, which is shaded. The perimeters of the rectangles are 15 and 21, and the perimeter of the triangle is 6. Quantity A:The sum of the lengths of the thick line segments Quantity B:30 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 8. x and y are integers.$$ 2^{x}-3y=20 $$Quantity A:y Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set1 9. If x is 50 percent of y and if z is 30 percent of y, where y>0 , then z is what percent of x ?_____% PPS2-Set1 10. A total of 36,000 was invested for one month in a new money market account that paid simple annual interest at the rate of r percent. If the investment earned 360 in interest for the month, what is the value of r ? • A . 10.0 • B . 10.5 • C . 11.0 • D . 12.0 • E . 12.5 PPS2-Set1 11. The equation$$C=\frac{5}{9}(F-32)$$represents the relationship between temperature C in degrees Celsius and the corresponding temperature F in degrees Fahrenheit. The graph shows the high temperature, in degrees Fahrenheit, on each day of a certain week. Which of the following is closest to the range of the high temperatures for the week, in degrees Celsius? • A . 4℃ • B . 7℃ • C . 8℃ • D . 12℃ • E . 14℃ PPS2-Set1 12. The circular bases of a right circular cylinder are inscribed in two opposite faces of a cube. If the volume of the cube is 64, which of the following is closest to the volume of the cylinder? • A . 46 • B . 50 • C . 54 • D . 58 • E . 62 PPS2-Set1 13. All of the students in an English class took a test, and each student received a test score that was a whole number between 60 and 100, inclusive. The table shows the number of students who received a test score in each of four score intervals. Which of the following numbers could be the median test score for all of the students? Indicate all such numbers. • A . 85 • B . 80 • C . 75 • D . 70 • E . 65 • F . 60 PPS2-Set1 14. For mass-market books in 2015, which of the following is closest to the ratio of the dollar amount of sales of adult hardcover books to the dollar amount of sales of juvenile hardcover books? • A . 7 to 2 • B . 5 to 2 • C . 4 to 1 • D . 3 to 1 • E . 2 to 1 PPS2-Set1 15. PPS2-Set1 16. If the sales of mass-market adult hardcover books accounted for 33 percent of mass-market book sales in 2010, by approximately what percent did the dollar amount of sales of this type of book increase from 2010 to 2015 ? • A . 20% • B . 30% • C . 40% • D . 50% • E . 60% PPS2-Set1 17. In a study of online news sources, computer users were surveyed to determine what computer sources they used for online news. The responses of those surveyed are summarized in the table shown. If 15 percent of those surveyed responded that they used both newspaper and magazine websites, what percent of those surveyed used newspaper websites but not magazine websites? _____% PPS2-Set1 18. The circumference of circle X is 24π. If the radius of circle Y is equal to$$\frac{1}{12}$$of the circumference of circle X, what is the circumference of circle Y ? • A . π • B . 2π • C .$$2π^{2}$$• D .$$4π^{2}$$• E .$$2π^{3}$$PPS2-Set1 19. If t≠0, which of the following is equivalent to$$\frac{1}{1+\frac{1}{t+\frac{1}{t}}}$$? • A .$$\frac{1}{t}$$• B .$$\frac{t}{t^{2}+1}$$• C .$$\frac{t^{2}+1}{t}$$• D .$$\frac{t}{t^{2}+t+1}$$• E .$$\frac{t^{2}+1}{t^{2}+t+1}$$PPS2-Set1 20. 6≤|x|≤8 1≤|y|≤2 3≤|z|≤4 If x, y, and z satisfy the inequalities shown, what is the least possible value of |x+y+z| ? • A . 0 • B . 1 • C . 2 • D . 3 • E . 4 Download PPS2-Set1 Quant Answers ## PPS2-Set2 PPS2-Set2 1. |x|+|y|=3 Quantity A:x+y Quantity B:-2 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 2. The sum of 11 consecutive integers is 22. Quantity A: The median of the 11 integers Quantity B:3 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 3. When the positive integer q is divided by 2, the remainder is 0. Quantity A:The remainder when q is divided by 8 Quantity B:4 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 4. Figure I and Figure II each show a small square inscribed in a large square that has sides of length 10. Quantity A: The perimeter of the small square in Figure I Quantity B: The perimeter of the small square in Figure II • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 5. Quantity A: The area of a circle with circumference 8πx Quantity B: The area of a circle with radius 4x • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 6. A certain car travels 120 miles in t hours at a constant rate of r miles per hour. Quantity A: The number of hours required for the car to travel 240 miles at a constant rate of 3r miles per hour Quantity B:t • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 7. • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set2 8. If x=-3, which of the following is greatest? • A . 1+x • B . x-5 • C .$$\frac{1}{x}$$• D . 3x • E .$$x^{3}$$PPS2-Set2 9. A class contains 120 students, each of whom is either a part-time student or a full-time student. If a student is to be selected at random from the class, then the probability that the student will be a part-time student is$$\frac{2}{5}$$. How many of the students in the class are full-time students? • A . 24 • B . 48 • C . 60 • D . 72 • E . 96 PPS2-Set2 10. The least positive integer that is divisible by 2, 3, 15, and 28 is • A . 210 • B . 420 • C . 840 • D . 1,260 • E . 2,520 PPS2-Set2 11. In a certain city, 15 percent of the total population is more than 60 years old. If 60 percent of the people older than 60 voted in a recent election, then these voters comprised what percent of the total population? • A . 6% • B . 8% • C . 9% • D . 15% • E . 60% PPS2-Set2 12. According to the scale given on a certain map, 1 inch is equivalent to 20 miles. Which of the following scales are the same as the scale given on the map? Indicate all such scales. • A .$$\frac{1}{4}$$inch is equivalent to 5 miles. • B .$$\frac{1}{2}$$inch is equivalent to 10 miles. • C .$$\frac{5}{2}$$inches are equivalent to 50 miles. • D . 4 inches are equivalent to 80 miles. PPS2-Set2 13. If x is an odd integer, which of the following must be an odd integer? • A .$$x^{4}+1$$• B .$$x^{4}-1$$• C .$$(x+1)^{5}-2$$• D .$$(x+1)^{5}+1$$• E .$$(x+1)^{6}+2$$PPS2-Set2 14. For the countries shown, what is the range of the percents of 25 to 64 year olds with no high school diploma? • A . 52% • B . 59% • C . 63% • D . 68% • E . 69% PPS2-Set2 15. For how many of the countries was the percent of 25 to 64 year olds with no high school diploma greater than the percent with a two-year college degree or higher? • A . Three • B . Four • C . Five • D . Six • E . Seven PPS2-Set2 16. What is the median unemployment rate for 25 to 64 year olds in those countries for which more than 15 percent of 25 to 64 year olds had a level of educational attainment of a two-year college degree or higher? • A . 5.6% • B . 6.2% • C . 6.8% • D . 7.8% • E . 8.8% PPS2-Set2 17. Country X consists of five regions-P, Q, R, S, and T. The circle graphs show the percent distributions of the population and the area of Country X, by region. Which region of Country X has the greatest population per unit of area? • A . P • B . Q • C . R • D . S • E . T PPS2-Set2 18. Which two of the following points in the -plane lie on the same horizontal line? Indicate both of the points. • A . (3,4) • B . (6,8) • C . (4,5) • D . (5,4) • E . (6,2) PPS2-Set2 19. In the figure shown, X is the midpoint of line segment VZ, and W and Y are the midpoints of line segments VX and XZ, respectively. What is the ratio of the length of VY to the length of WY ? • A . 2 to 1 • B . 2 to 3 • C . 3 to 2 • D . 3 to 4 • E . 4 to 3 PPS2-Set2 20. The sum of the squares of three consecutive positive integers is 149. What is the sum of the three integers?_____ Download PPS2-Set2 Quant Answers ## PPS2-Set3 PPS2-Set3 1. x and y are integers and xy<0. Quantity A:$$x^{y}$$Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 2. A certain ship traveled 40 miles at an average speed of 18 knots. (Note: 1 knot = 1.15 miles per hour, rounded to the nearest 0.01 mile.) Quantity A: The time it took the ship to travel the 40 miles Quantity B:2 hours • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 3. In RST, the measure of angle S is 52°, and the measure of angle T is 58°. #### Quantity A The length of side RS #### Quantity B The length of side ST • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 4. 15 < x < 30 15 < y < 30 15 < z < 30 Quantity A:The range of the three numbers x, y, and z Quantity B:15 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 5. 0 < x < y < 1 Quantity A:$$(\frac{\sqrt{x}}{y^3})^{-1}$$Quantity B:$$(\frac{\sqrt{y}}{x^3})^{-1}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 6. In the xy-plane shown, point R (not shown) has coordinates (c,d), where c>0. The area of triangle PQR is 24. Quantity A:c Quantity B:2 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 7.$$x^{2}y^{3}$$< 0 Quantity A:$$xy^{2}$$Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set3 8. Consider dates represented by three numbers in the form day-month-year. For example, 21-3-2000 represents March 21, 2000. A date in which the day, month, and year are each divisible by 5 is called a "triple-five date." How many triple-five dates were there in the year 2010 ? • A . 6 • B . 9 • C . 10 • D . 11 • E . 12 PPS2-Set3 9. If the average (arithmetic mean) of three consecutive integers is 2 more than the average of 18, 27, and 30, what is the greatest of the three consecutive integers? • A . 26 • B . 27 • C . 28 • D . 30 • E . 75 PPS2-Set3 10. Each of the marbles in a bag is either blue, red, or green, and there is at least one marble of each color in the bag. If the bag contains twice as many blue marbles as red marbles, then the number of red marbles in the bag divided by the total number of marbles in the bag is • A . less than$$\frac{1}{3}$$• B . equal to$$\frac{1}{3}$$• C . between$$\frac{1}{3}$$and$$\frac{1}{2}$$• D . between$$\frac{1}{2}$$and 2 • E . greater than 2 PPS2-Set3 11. The circumference of circle$$C_{1}$$is 12π and the circumference of circle$$C_{2}$$is 24π. What is the ratio of the area of$$C_{2}$$to the area of$$C_{1}$$? • A . 2 to 1 • B . 3 to 1 • C . 4 to 1 • D . 6 to 1 • E . 8 to 1 PPS2-Set3 12. In the rectangular coordinate system, line k has slope$$\frac{1}{2}$$and y-intercept 4. What is the x-intercept of k ? • A . -8 • B . -2 • C .$$\frac{1}{2}$$• D . 2 • E . 8 PPS2-Set3 13. Each of two generators produces energy at a constant rate, but the two rates are different. One of the generators produces n units of energy in 4 hours, and the other generator produces the same amount of energy in half the time. What fraction of n units of energy will be produced by both generators if they work simultaneously for 40 minutes? • A .$$\frac{3}{8}$$• B .$$\frac{1}{2}$$• C .$$\frac{5}{8}$$• D .$$\frac{3}{4}$$• E .$$\frac{7}{8}$$PPS2-Set3 14. Distribution of Responses of 2,000 Residents to Two Library Funding Questions Question 1: To the best of your knowledge, the largest amount of funding for public libraries is provided by what source? Question 2: In your opinion, the largest amount of funding should be provided by what source? The number of residents who chose "Private donations" as a response to question 1 was how many more than the number who chose "Private donations" as a response to question 2 ? • A . 232 • B . 218 • C . 194 • D . 168 • E . 128 PPS2-Set3 15. Distribution of Responses of 2,000 Residents to Two Library Funding Questions Question 1: To the best of your knowledge, the largest amount of funding for public libraries is provided by what source? Question 2: In your opinion, the largest amount of funding should be provided by what source? If one resident is to be randomly selected from among the 2,000 residents, what is the probability that the selected residents response to question 2 was either "Local government" or "Private donations"? • A .$$\frac{1}{4}$$• B .$$\frac{2}{7}$$• C .$$\frac{1}{3}$$• D .$$\frac{2}{5}$$• E .$$\frac{1}{2}$$PPS2-Set3 16. Distribution of Responses of 2,000 Residents to Two Library Funding Questions Question 1: To the best of your knowledge, the largest amount of funding for public libraries is provided by what source? Question 2: In your opinion, the largest amount of funding should be provided by what source? What is the greatest possible number of residents who chose the response "Local government" to both questions? • A . 94 • B . 320 • C . 414 • D . 640 • E . 740 PPS2-Set3 17. Marcel purchased a television at a price that was less than its list price. The total amount that he paid for the television consisted of the purchase price and a sales tax of 7.20, which was p percent of the purchase price. Which of the following statements individually provide(s) sufficient additional information to determine the value of p ? Indicate all such statements. • A . The total amount that Marcel paid for the television was 127.20. • B . The purchase price of the television was 40.00 less than the list price. • C . The purchase price of the television was 25 percent less than the list price. PPS2-Set3 18. How many integers between 1 and 100 are multiples of 7 but are not multiples of 6 ?_____ PPS2-Set3 19. If$$\frac{1}{2}$$< x <$$\frac{3}{4}$$and$$\frac{2}{7}$$< y <$$\frac{4}{7}$$, which of the following is a possible value of xy ? • A .$$\frac{1}{7}$$• B .$$\frac{2}{7}$$• C .$$\frac{3}{7}$$• D .$$\frac{4}{7}$$• E .$$\frac{5}{7}$$PPS2-Set3 20. The function g is defined for all numbers x by g(x)=r$$x^{5}$$- s$$x^{3}$$+t, where r, s, and t are constants. If g(1)=0, which of the following could be the values of the three constants? Indicate all such values. • A . r=3,s=2 and t=-1 • B . r=-4,s=3 and t=1 • C . r=-2,s=-1 and t=1 • D . r=4,s=3 and t=-7 • E . r=4,s=-3 and t=-7 Download PPS2-Set3 Quant Answers ## PPS2-Set4 PPS2-Set4 1. List K consists of the four numbers w, x, y, and z. List M consists of the four numbers w+5,x+5 ,y+5 , and z+5. Quantity A: The standard deviation of the numbers in list K Quantity B: The standard deviation of the numbers in list M • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 2. A car traveled at a constant speed of 48 kilometers per hour for 3 kilometers. Quantity A: The time, in minutes, it took for the car to travel the 3 kilometers Quantity B: 3.75 minutes • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 3. • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 4.$$x=\frac{1}{2}$$Quantity A:5x^{-3} - 9x^{-2} Quantity B:4 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 5. In the figure shown, hexagon PQRSTU is equilateral and is inscribed in the circle with center O. Quantity A: The length of diameter UOR Quantity B: The length of arc RST • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 6. Quantity A:$$(r+s)^{2}$$Quantity B:$$r^{2}+s^{2}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 7. x>2 and y<0 Quantity A:|xy|-x Quantity B:xy • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS2-Set4 8. Ben has 30 pencils in a box. Each of the pencils is one of 5 different colors, and there are 6 pencils of each color. If Ben selects pencils one at a time from the box without being able to see the pencils, what is the minimum number of pencils that he must select in order to ensure that he selects at least 2 pencils of each color? • A . 24 • B . 25 • C . 26 • D . 27 • E . 28 PPS2-Set4 9. The price of a package of notebooks is$$\frac{1}{3}$$more at Store A than at Store B. If the difference in these prices is 0.35, what is the price at Store A ? • A . 0.70 • B . 1.05 • C . 1.40 • D . 1.75 • E . 2.45 PPS2-Set4 10. The circumference of circle C is equal to the perimeter of square S. If the area of the circle is z, which of the following represents the area of the square, in terms of z ? • A .$$\frac{π}{4z}$$• B .$$\frac{4}{zπ}$$• C .$$\frac{zπ}{4}$$• D .$$\frac{4π}{z}$$• E .$$\frac{4z}{π}$$PPS2-Set4 11.$$\frac{7}{3°}$$,$$\frac{7}{4°}$$,$$\frac{7}{5°}$$,... The first term of the infinite sequence shown is$$\frac{7}{3°}$$, and each term thereafter has a numerator of 7 and a denominator that is 1 greater than the denominator of the preceding term. Which of the following terms of the sequence is equal to the 6th term of the sequence minus the 7th term of the sequence? • A . 40th • B . 42nd • C . 44th • D . 70th • E . 72nd PPS2-Set4 12. In the figure shown, OP is a diameter of the circle. What is the x-coordinate of point P ? • A . -3 • B . -6 • C .$$-\sqrt{3}$$• D .$$-2\sqrt{3}$$• E .$$-3\sqrt{3}$$PPS2-Set4 13. The odds in favor of the occurrence of event A are defined to be the ratio of the probability of A occurring to the probability of A not occurring. Past records indicate that the odds in favor of a shipment from Company Z arriving on the specified date are 3 to 7. On the basis of this record, what is the probability that a shipment from Company Z will not arrive on the specified date? • A .$$\frac{3}{10}$$• B .$$\frac{4}{10}$$• C .$$\frac{7}{10}$$• D .$$\frac{3}{7}$$• E .$$\frac{4}{7}$$PPS2-Set4 14. Parking Tickets Issued to Drivers in Town X in February 2017 (Total number of tickets issued: 420) To the nearest whole percent, the number of drivers who were issued 3 parking tickets is what percent greater than the number who were issued 4 or more tickets? • A . 4% • B . 9% • C . 10% • D . 11% • E . 16% PPS2-Set4 15. Parking Tickets Issued to Drivers in Town X in February 2017 (Total number of tickets issued: 420) What is the average (arithmetic mean) number of parking tickets issued to the drivers who were issued 6 or more tickets? • A . 7.0 • B . 7.5 • C . 8.0 • D . 8.5 • E . 9.0 PPS2-Set4 16. Parking Tickets Issued to Drivers in Town X in February 2017 (Total number of tickets issued: 420) For the drivers who were issued parking tickets, what is the median number of tickets issued per driver? • A . 2.0 • B . 2.5 • C . 3.0 • D . 3.5 • E . 4.0 PPS2-Set4 17. In the figure shown, seven small circles of equal diameter are located inside a large circle. Each of the six outer small circles is tangent to the small circle in the center, to two other adjacent small circles, and to the large circle. If the diameter of the large circle is D, then the sum of the areas of the unshaded regions inside the large circle is equal to which of the following? • A .$$\frac{πD^{2}}{36}$$• B .$$\frac{πD^{2}}{18}$$• C .$$\frac{πD^{2}}{9}$$• D .$$\frac{πD^{2}}{2}$$• E .$$\frac{7πD^{2}}{4}$$PPS2-Set4 18. Of the students enrolled at University U in the fall of 2008,$$\frac{3}{8}$$were sophomores and$$\frac{1}{50}$$were biology majors. Which of the following could be the number of students enrolled at University U in the fall of 2008 ? Indicate all such numbers. • A . 7,000 • B . 7,040 • C . 7,050 • D . 7,100 • E . 7,125 • F . 7,200 PPS2-Set4 19. If 3x+y=2, 3x+2y=0, and x-2z=1, what is the value of z ? Give your answer as a fraction. z=_____ PPS2-Set4 20. When the positive integer N is divided by 16, the remainder is 3. Which of the following integers could be the remainder when N is divided by 6 ? Indicate all such integers. • A . 0 • B . 1 • C . 2 • D . 3 • E . 4 • F . 5 Download PPS2-Set4 Quant Answers ## PPS3-Set1 PPS3-Set1 1. Quantity A:$$2^{x+2}$$Quantity B:$$(4)(2^{x})$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 2. x is a negative integer. Quantity A:$$x^{2x}$$Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 3. t>0 x<2t y>5t Quantity A:$$\frac{y-x}{3}$$Quantity B: t • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 4. Point O is the center of the circle. Line segment OT and arc RST both have length 4. Quantity A:x Quantity B:60 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal.. • D . The relationship cannot be determined from the information given. PPS3-Set1 5.$$y=2x^{2}+3$$Quantity A:In the equation, the number of y-values that correspond to each x-value Quantity B:2 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 6. x≠1 Quantity A:$$\frac{x^{2}-2}{x-1}$$Quantity B:x+2 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 7.$$(x+y)^{2}=25$$Quantity A:The average (arithmetic mean) of x and y Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 8. Quantity A: The standard deviation of the heights of 12 people whose heights range from 62 inches to 74 inches, inclusive Quantity B: The standard deviation of the heights of 12 people whose heights range from 60 inches to 72 inches, inclusive • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set1 9. If a company required a total storage capacity equal to the combined storage capacity of 16 small sheds, which of the following rentals would cost the least per week for the companys storage capacity requirements? • A . 4 medium sheds and 4 small sheds • B . 5 medium sheds and 1 small shed • C . 1 large shed and 4 medium sheds • D . 2 large sheds, 2 medium sheds, and 2 small sheds • E . 3 large sheds, 1 medium shed, and 1 small shed PPS3-Set1 10. In the figure, ABCD is a square, E is the midpoint of side AD, and F is the midpoint of side BC. The area of the shaded region is what fraction of the area of square region ABCD ? • A .$$\frac{1}{8}$$• B .$$\frac{1}{6}$$• C .$$\frac{1}{5}$$• D .$$\frac{1}{4}$$• E .$$\frac{1}{3}$$PPS3-Set1 11. When the integer n is divided by 20, the remainder is 15. Which of the following must be a divisor of n ? • A . 3 • B . 5 • C . 6 • D . 7 • E . 10 PPS3-Set1 12. Twenty-three cards are numbered consecutively from 1 through 23. If one card is to be randomly selected from the 23 cards, what is the probability that the number on the selected card will be a multiple of 3 or a multiple of 4 or a multiple of both 3 and 4 ? • A .$$\frac{7}{23}$$• B .$$\frac{9}{23}$$• C .$$\frac{11}{23}$$• D .$$\frac{12}{23}$$• E .$$\frac{13}{23}$$PPS3-Set1 13. In the figures shown, ABCD is a square with sides of length 12, and EFGH is a square with sides of length 9. If the ratio of the area of square ABCD to the area of square EFGH is equal to the ratio of the area of triangle PCD to the area of triangle QGH, what is the ratio of the length of PC to the length of QG ? Give your answer as a fraction. _____ PPS3-Set1 14. Which of the following is closest to the fraction of the world population who were Internet users? • A .$$\frac{1}{20}$$• B .$$\frac{1}{10}$$• C .$$\frac{1}{5}$$• D .$$\frac{1}{3}$$• E .$$\frac{1}{2}$$PPS3-Set1 15. • A . Africa • B . Asia • C . Europe • D . Latin America/Caribbean • E . North America PPS3-Set1 16. The number of Internet users in Europe and Asia was closest to what percent of the world population? • A . 13.3% • B . 44.6% • C . 65.4% • D . 68.6% • E . 70.9% PPS3-Set1 17. At 12:00 noon a hose began draining water from a pool at a constant rate of 120 ounces per minute. At 2:00 that afternoon, an additional hose began draining water from the pool, increasing the constant rate at which the water was being drained to 240 ounces per minute. The pool was empty before 4:30 that afternoon. Which of the following could have been the amount of water, in ounces, in the pool at 12:00 noon that day? Indicate all such amounts. • A . 42,640 • B . 46,080 • C . 50,250 • D . 52,540 • E . 55,320 PPS3-Set1 18. The sequence of numbers$$C_{1},C_{2},C_{3},...C_{n}...$$is defined by$$C_{1}=2,C_{2}=4$$and$$C_{n}=C_{n-1}+n$$for each integer n greater than 2. What is the value of$$C_{6}$$? • A . 12 • B . 17 • C . 18 • D . 22 • E . 24 PPS3-Set1 19. The table shows the frequency distribution of the random variable X. What is the median of the distribution of the values of X ? • A . 1.0 • B . 1.8 • C . 2.0 • D . 2.5 • E . 3.0 PPS3-Set1 20. A product is on sale for a discounted price that is 20 percent less than its regular price. The regular price is what percent greater than the discounted price? _____% Download PPS3-Set1 Quant Answers ## PPS3-Set2 PPS3-Set2 1. Of all the students in a classroom,$$\frac{1}{3}$$have brown eyes and$$\frac{1}{4}$$of the rest of the students have green eyes. Quantity A: The fraction of the students in the classroom who have green eyes Quantity B:$$\frac{1}{12}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 2. Quantity A: The average (arithmetic mean) of the 5 consecutive integers between 5 and 11 Quantity B: The median of the 5 consecutive integers between 5 and 11 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 3. The length of each side of square S is 10. The length of each edge of cube T is 4. Quantity A:The area of square S Quantity B:The surface area of cube T • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 4. n is a positive integer.$$n^{2}+2n$$is even. Quantity A:$$(-1)^{n}$$Quantity B:$$(-1)^{n-1}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 5. Quantity A:The perimeter of Quantity B:The perimeter of • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 6. Quantity A:In the xy-plane, the distance from the point (-5,-3) to the point (-2,-5) Quantity B:In the xy-plane, the distance from the point (3,4) to the point(6,2) • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 7. x is a number greater than 0. Quantity A:$$\frac{x}{x}$$Quantity B:$$\frac{x}{1}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set2 8. A certain saleswoman earns 4 for each hour worked plus a 10 percent commission on her total sales. In June she worked 240 hours and had total sales of 40,400. What percent of the money she earned in June was commission? • A . 78.0% • B . 79.2% • C . 80.0% • D . 80.8% • E . 88.0% PPS3-Set2 9. If the speed of a vehicle was reduced from 65 miles per hour to 35 miles per hour, by approximately how many kilometers per hour was the speed reduced? (1 kilometer = 0.62 mile, rounded to the nearest 0.01 mile) • A . 16 • B . 22 • C . 40 • D . 48 • E . 56 PPS3-Set2 10. a < 8 < a+8 < 2a+4 <$$a^{2} - 20$$If a is an integer that satisfies the inequalities shown, what is the value of a ? a=_____ PPS3-Set2 11. A total of 72,000 was invested for one month in a new money market account that paid simple annual interest at the rate of r percent. If the investment earned 360 in interest for the month, what is the value of r ? • A . 3 • B . 6 • C . 9 • D . 10 • E . 12 PPS3-Set2 12. Set A consists of four consecutive integers. Set B consists of all integers that result from adding 2 to each of the integers in set A together with all integers that result from subtracting 2 from each of the integers in set A. How many more integers are in set B than in set A ? • A . 1 • B . 2 • C . 3 • D . 4 • E . 8 PPS3-Set2 13. In the figure above, if line KL is parallel to line PN, what is the value of x ? • A . 105 • B . 120 • C . 135 • D . 150 • E . It cannot be determined from the information given. PPS3-Set2 14. For how many of the seven categories did the value of exports increase by more than 50 percent from 2002 to 2003 ? • A . Two • B . Three • C . Four • D . Five • E . Six PPS3-Set2 15. Approximately what was the percent increase in the value of the total exports from 2002 to 2003 ? • A . 10% • B . 20% • C . 30% • D . 40% • E . 50% PPS3-Set2 16. PPS3-Set2 17.$$m=\frac{n^{2}-25}{100}$$If n is a 2-digit integer with units digit 5 in the equation shown, which of the following could be the units digit of m ? • A . 1 • B . 3 • C . 5 • D . 6 • E . 8 PPS3-Set2 18. List K: a, b, c, d, e List K consists of five numbers such that 0 < a < b < c < d < e. Which of the following statements must be true? Indicate all such statements. • A . The range of the numbers in list K is e. • B . The median of the numbers in list K is c. • C . The average (arithmetic mean) of the numbers in list K is c. PPS3-Set2 19. Which of the following lists has the greatest standard deviation? • A . 10, 20, 30, 40, 50 • B . 10, 30, 30, 30, 50 • C . 10, 25, 30, 35, 50 • D . 10, 10, 30, 50, 50 • E . 20, 20, 30, 40, 40 PPS3-Set2 20. An item was on sale for a discounted price that was p percent less than the regular price of 50. A customer purchased the item at the discounted price and used a coupon valued at k dollars to pay for part of the item. If the discounted price was equal to the value of the coupon plus 20, which of the following could be the values of p and k ? Indicate all such values. • A . p=10 and k=20 • B . p=10 and k=25 • C . p=20 and k=10 • D . p=20 and k=20 • E . p=30 and k=15 Download PPS3-Set2 Quant Answers ## PPS3-Set3 PPS3-Set3 1. The price of a certain coat is discounted by x percent, and the new price is then discounted by y percent, resulting in price p. Quantity A:Price p if x=10 and y=30 Quantity B:Price p if x=20 and y=20 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 2. s, t, and u are integers, and 10≤s<><> Quantity A:$$s+\frac{t}{u}$$Quantity B:11 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 3. Quantity A:x Quantity B:60 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 4. The function f is defined by$$f_{(x)}=x^{-100}$$for all nonzero numbers x. Quantity A:$$f_{(2)}$$Quantity B:$$f_{(-2)}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 5. m is the least positive integer for which 18m can be expressed as the square of an integer. n is the least positive integer for which 9n can be expressed as the cube of an integer. Quantity A:m Quantity B:n • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 6. Quantity A:$$\frac{50!}{(25!)(25!)}$$Quantity B:$$\frac{50!}{(24!)(26!)}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 7. 3x+4y=2 6x+8y=4 Quantity A:x Quantity B:y • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set3 8. Which of the following discounts on a certain computer, when applied to the regular price of 1,200, are equivalent to a 30 percent discount off the regular price of that computer? Indicate all such discounts. • A . A 360 discount • B . A 20 percent discount followed by a 10 discount • C . A 25 percent discount followed by a 60 discount PPS3-Set3 9. At a local election there were two propositions on the ballot, R and S. Twice as many voters voted "yes" for R as for S. If the number who voted "yes" for R but "no" for S was 750 and the number who voted "yes" for S but "no" for R was 310, how many voted "yes" for both propositions? • A . 122 • B . 127 • C . 130 • D . 135 • E . 140 PPS3-Set3 10. Of the x members of a certain club,$$\frac{3}{8}$$are men and$$\frac{2}{9}$$of the men are over 50 years old. If 4 men in the club are over 50 years old, what is the value of x? • A . 48 • B . 68 • C . 72 • D . 96 • E . 136 PPS3-Set3 11. A storage trunk contains 6 identical blankets and 3 identical pillows. The weight of each blanket is 3 times the weight of each pillow. What is the ratio of the total weight of the 6 blankets to the total weight of the 3 pillows? • A . 2 to 1 • B . 3 to 1 • C . 6 to 1 • D . 9 to 1 • E . 18 to 1 PPS3-Set3 12. What is the perimeter of polygon ABCDE above? • A . 34 • B .$$12\sqrt{2}+17$$• C .$$12\sqrt{2}+22$$• D .$$12\sqrt{3}+17$$• E .$$12\sqrt{3}+22$$PPS3-Set3 13. Which of the following is equivalent to (a-b)-(c-d) ? • A . (a-b)+(-c-d) • B . (a-c)+(b-d) • C . (a+c)-(b+d) • D . (a-d)+(b-c) • E . (a+d)-(b+c) PPS3-Set3 14. For the years shown, what was the median of the companys sales, in thousands of dollars? • A . 46.4 • B . 48.5 • C . 52.0 • D . 57.6 • E . 58.8 PPS3-Set3 15. Which of the following is closest to the average (arithmetic mean) sales of the company for the 3 years that the company experienced its greatest earnings? • A . 59,000 • B . 60,000 • C . 62,000 • D . 65,000 • E . 67,000 PPS3-Set3 16. The companys sales in 1996 were approximately what percent greater than its sales in 1995 ? • A . 10% • B . 30% • C . 50% • D . 70% • E . 90% PPS3-Set3 17. The figure shows the graphs, in the xy-plane, of the equations y=ax+b and y=cx+k, where a, b, c, and k are constants. Which of the following statements must be true? Indicate all such statements. • A . c< a • B . c> a • C . k< b • D . k> b PPS3-Set3 18. A list of 42 numbers has an average (arithmetic mean) of 110.0. A second list of 58 numbers has an average of 150.0. What is the average of the 100 numbers in the two lists combined? _____ PPS3-Set3 19. The volume of a large cube is twice the volume of a small cube. If the length of an edge of the small cube is 2, what is the length of an edge of the large cube? • A . 4 • B . 8 • C .$$2\sqrt[3]{2}$$• D .$$4\sqrt[3]{2}$$• E .$$8\sqrt[3]{2}$$PPS3-Set3 20. The average (arithmetic mean) of x,x+2 ,x+4, and x+6 is 6. What is the average of$$x^{2}$$,$$(x+2)^{2}$$,$$(x+4)^{2}$$, and$$(x+6)^{2}$$? • A . 30 • B . 36 • C . 41 • D . 49 • E . 52 Download PPS3-Set3 Quant Answers ## PPS3-Set4 PPS3-Set4 1. y≥0 Quantity A:$$(\sqrt{y+5}-\sqrt{y})(\sqrt{y+5}+\sqrt{y})$$Quantity B:5 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 2. In the xy-plane, the graph of$$y=g_{(x)}$$intersects the x-axis at 3 points. Quantity A:The number of points at which the graph of$$y=g_{(x-5)}$$intersects the x-axis Quantity B:3 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 3. m and n are positive integers. n and n+2 are factors of m. Quantity A:$$\frac{m}{n}$$Quantity B:n+2 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 4. x>7,999 Quantity A:The digit in the thousands place of x Quantity B:6 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 5. n is a negative integer, and p is a positive integer. Quantity A:The product of the integers from n to p, inclusive Quantity B:0 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 6. x percent of y is$$\frac{3}{4}$$of z, where xyz≠0 . Quantity A:$$\frac{xy}{z}$$Quantity B:75 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 7. Quantity A:x Quantity B:85 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS3-Set4 8. In the figure above, the circles centered at$$O_{1}$$and$$O_{2}$$have radii of equal length. If$$O_{1}O_{2}=9$$and AB=3, what is the circumference of the circle centered at$$O_{1}$$? • A . 6π • B . 9π • C . 12π • D . 18π • E . 36π PPS3-Set4 9. If n is an integer, what is the least value of n for which$$4^{-n}<\frac{1}{512}$$? • A . 4 • B . 5 • C . 6 • D . 7 • E . 8 PPS3-Set4 10. On the outside, a closed rectangular packing box, made out of cardboard, is 12 inches long, 18 inches wide, and 24 inches high. If the cardboard is$$\frac{1}{4}$$inch thick, which of the following is closest to the volume inside the box, in cubic inches? • A . 3,700 • B . 3,900 • C . 4,300 • D . 4,700 • E . 5,200 PPS3-Set4 11. In the xy-plane above, what is the area of quadrilateral OABC ? • A . 15 • B .$$13\frac{1}{2}$$• C .$$11\frac{1}{4}$$• D .$$10\frac{1}{2}$$• E . 7 PPS3-Set4 12. The average (arithmetic mean) ages, in years, of the people in group A and group B are 41 and 36, respectively. The average age, in years, of the people in the two groups combined is 38. If there are no people in both group A and group B, what fraction of the people in the two groups combined are in group B? • A .$$\frac{2}{5}$$• B .$$\frac{1}{2}$$• C .$$\frac{3}{5}$$• D .$$\frac{2}{3}$$• E .$$\frac{3}{4}$$PPS3-Set4 13. How many integers n between 100 and 299 are there such that the hundreds digit of n is less than the tens digit of n and the tens digit of n is less than the units digit of n ? • A . 48 • B . 49 • C . 50 • D . 51 • E . 52 PPS3-Set4 14. What is the range of the average costs for the eight home remodeling projects listed? • A . 24,100 • B . 24,700 • C . 25,400 • D . 26,100 • E . 26,800 PPS3-Set4 15. In City X, the percent increase from 1997 to 1999 in the average cost of a deck addition was 45 percent, and the percent increase from 1994 to 1997 in the average cost of a deck addition was 26 percent. Which of the following expressions represents the average cost, in dollars, of a deck addition in City X in 1994 ? • A . (1.45)(1.26)(9,100) • B . (0.45)(0.26)(9,100) • C .$$\frac{(1.26)(9,100)}{1.45}$$• D .$$\frac{(9,100)}{(1.45)(1.26)}$$• E .$$\frac{(9,100)}{(0.45)(0.26)}$$PPS3-Set4 16. For how many of the remodeling projects listed is the average return on the project when the home is sold less than 75 percent of the average cost of the project? • A . Three • B . Four • C . Five • D . Six • E . Seven PPS3-Set4 17. A grocery store had 105 pieces of fruit for sale consisting of apples, mangoes, and peaches. Which of the following statements individually provide(s) sufficient additional information to determine the number of apples for sale at the grocery store? Indicate all such statements. • A . The total number of apples and peaches was 62. • B . The ratio of the number of apples to the total number of mangoes and peaches was 1 to 6. • C . The ratio of the number of mangoes to the number of peaches was 43 to 47. PPS3-Set4 18. Of the 36 students in a certain class, 10 are in the chess club and 13 are in the bridge club. If 20 of the students are not in either club, how many of the students are in only one of the two clubs? • A . 7 • B . 9 • C . 14 • D . 16 • E . 23 PPS3-Set4 19. x(x+3)(x-5)>0 Which of the following inequalities specify values of x that satisfy the inequality above? Indicate all such inequalities. • A . x<-3 • B .$$-3 < x < 0$$• C .$$0 < x < 5$$• D . x>5 PPS3-Set4 20. The figure shows a circle with center A and radius 10, and a circle with center D and radius 3. AD intersects the two circles at points F and E, respectively. Line is tangent to the two circles at points B and C, respectively. If the length of FE is 12, what is the length of BC ? Length of BC:_____ Download PPS3-Set4 Quant Answers ## PPS4-Set1 PPS4-Set1 1. x is a positive two-digit integer with units digit 6, and y is a positive two-digit integer with tens digit 8. #### Quantity A The least possible value of x+y #### Quantity B 96 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 2. Each of six consecutive positive integers is divided by 6. Quantity A: The average (arithmetic mean) of the 6 resulting remainders Quantity B: 3.5 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 3. x, y, and z are positive integers. 3x+2y+z=42 Quantity A:x+y+z Quantity B:18 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 4. The center of the circle is O and RS>ST. Quantity A:x Quantity B:y • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 5. m+t=1 m < t Quantity A:mt Quantity B:$$m^2$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 6. x is an integer. Quantity A:$$\frac{10^{3x+1}}{10^{x+3}}$$Quantity B:$$\frac{10^{x+1}}{10^{1-x}}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 7. #### Quantity A The number of possible values of the product pt, where p and t are even positive integers and 30< pt< 34 #### Quantity B 1 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 8. A submarines depth, in meters below sea level, at a time t minutes after it began to dive below the sea surface is equal to$$g_{(x)}$$for 0≤t≤6. Its diving speed, measured in meters per minute, is the rate of change in depth. #### Quantity A The average diving speed of the submarine for 0≤t≤3 #### Quantity B Quantity B:The average diving speed of the submarine for 3≤t≤6 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set1 9. The table shows the distribution of the grades on a chemistry exam taken by a class of 40 students. If one of the students is to be chosen at random, what is the probability that the student chosen will be one whose grade on the exam is greater than or equal to 90 ? Give your answer as a fraction. _____/_____ PPS4-Set1 10. In a certain store, notebooks that normally sell for 59 cents each are on sale for 2 for 99 cents. If a person buys 2x of these notebooks at the sale price, what is the value of x if the total amount saved compared to buying at the normal price is 95 cents? • A . 9 • B . 8 • C . 7 • D . 6 • E . 5 PPS4-Set1 11. List J: 5, 7, 9 List K: 4, 6, 8, 10 Set M will be created by choosing 2 different numbers from list J and 1 number from list K. How many different combinations of numbers are possible for set M ?_____ PPS4-Set1 12. If x is an integer, which of the following must be an even integer? • A .$$(x+1)^{2}$$• B . (x+1)(x+2) • C . (x+1)(x+3) • D .$$(x+2)^{2}$$• E . (x+2)(x+4) PPS4-Set1 13. Point B is the center of the circle, the circle is tangent to line , and the area of triangular region ABC is 18. What is the circumference of the circle? • A . 3π • B . 6π • C . 8π • D . 9π • E . 12π PPS4-Set1 14. For how many of the times at which readings were taken was the difference between the concentrations at the two heights greater than 50 parts per million? • A . One • B . Two • C . Three • D . Four • E . Five PPS4-Set1 15. For approximately how many hours was the concentration of carbon dioxide at 0.5 meter greater than or equal to the concentration at 0.2 meter? • A . 3 • B . 6 • C . 9 • D . 12 • E . 15 PPS4-Set1 16. The median of the 12 recorded concentrations at 0.2 meter is approximately how many parts per million? • A . 275 • B . 295 • C . 315 • D . 335 • E . 355 PPS4-Set1 17. The table shows the profit or loss that a travel company makes for rendering services to different numbers of passengers. If each additional passenger increases the profit, or decreases the loss, by the same dollar amount, what is the number of passengers for which the travel company will have neither a profit nor a loss? • A . 900 • B . 950 • C . 975 • D . 980 • E . 998 PPS4-Set1 18. Line segment AB is a diameter of the circle and has length 5. Points C and D are on the circle as shown. What is the area of the shaded region? • A . 24 • B . 16 • C . 14 • D . 12 • E . 6 PPS4-Set1 19. The volume of the interior of a rectangular storage bin is 240 cubic meters. If the perimeter of the interior base of the bin is 40 meters, which of the following could be the dimensions of the interior of the bin, in meters? Indicate all such dimensions. • A . 6 by 8 by 5 • B . 8 by 12 by 2.5 • C . 9 by 11 by 2.4 • D . 10 by 10 by 2.4 PPS4-Set1 20. The table shows the frequency distribution of the random variable Y. What is the median of the distribution of the values of Y ? • A . 1.0 • B . 1.3 • C . 1.5 • D . 1.7 • E . 2.0 Download PPS4-Set1 Quant Answers ## PPS4-Set2 PPS4-Set2 1. r>0 p is 75 percent of r. Quantity A:50 percent of p Quantity B:25 percent of r • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 2. From the cars manufactured in 2005 indicated in the table, one car is to be selected at random from the model A cars and one car is to be selected at random from the model B cars. Quantity A: The probability that the model A car selected will be one that required repairs in its first year Quantity B: The probability that the model B car selected will be one that required repairs in its first year • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 3. x>0 Quantity A:$$\frac{x}{x+1}$$Quantity B:$$\frac{x+1}{x+2}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 4. In the xy-plane, P and Q are two points on the line with equation y=2x+1. The x-coordinates of P and Q are 2 and 6, respectively. Quantity A:The length of line segment PQ Quantity B:9 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 5. In the circle with center G, arc MKN has length$$\frac{8}{3}π$$. In the circle with center J, arc PQR has length$$\frac{16}{3}π$$. Quantity A:a Quantity B:b • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 6. y+2<0 Quantity A:$$\frac{|y|}{y}$$Quantity B:-2 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 7. On the number line shown, a and b are the coordinates of two points. Quantity A:ab Quantity B:-ab • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set2 8. A small company made a profit of 9,000 last quarter. The dollar amount of the profit was distributed equally among the 4 divisions of the company. If each division distributed its dollar amount of the profit equally among the people in the division, how much more money did a person in a division of 6 people receive than a person in a division of 10 people? _____ PPS4-Set2 9. In a social group 62 members enjoy dancing and 28 members enjoy hiking. If each of the 75 members in the group enjoys dancing or hiking, how many members enjoy both dancing and hiking? • A . 13 • B . 15 • C . 28 • D . 34 • E . 47 PPS4-Set2 10. On each of the first 15 days of April, Aaron spent 5 percent of his monthly income for April. If at the end of the 15th day of April, he had 1,250 of his monthly income remaining, what was his monthly income for April? • A . 5,000 • B . 6,250 • C . 7,500 • D . 10,000 • E . 25,000 PPS4-Set2 11. A school stadium contains 2,000 seats. For a certain game, student tickets cost 3 each and nonstudent tickets cost 6 each. What is the least number of nonstudent tickets that must be sold so that the total ticket sales will be at least 8,400 ? • A . 400 • B . 800 • C . 900 • D . 1,200 • E . 1,600 PPS4-Set2 12. If r, s, and t are consecutive positive integers and r< s< t, which of the following statements must be true? Indicate all such statements. • A . s is a multiple of 2. • B . s is the average (arithmetic mean) of r and t. • C . s is the average (arithmetic mean) of r, s, and t. PPS4-Set2 13. 26, 29, 32, 33, 36, 37, 41, 42, 48, 50 The 10 numbers in list M (not shown) are determined by multiplying each of the 10 numbers in the list above by 5 and then subtracting 20 from each product. How many times greater is the range of the numbers in list M than the range of the numbers in the list above? _____times greater PPS4-Set2 14. In which of the following years was the number of foreign-born residents greatest? • A . 1900 • B . 1920 • C . 1940 • D . 1960 • E . 1980 PPS4-Set2 15. From 1960 to 1980, the total population increased by approximately what percent? • A . 5% • B . 15% • C . 25% • D . 35% • E . 45% PPS4-Set2 16. The ratio of the number of foreign-born residents in 1900 to the number of foreign-born residents in 1980 is closest to which of the following? • A . 1 to 2 • B . 1 to 3 • C . 2 to 3 • D . 2 to 5 • E . 3 to 2 PPS4-Set2 17. The sides of a triangle have lengths 7.5, 11, and x. If x is an integer, what is the least possible value of x ? • A . 1 • B . 2 • C . 3 • D . 4 • E . 5 PPS4-Set2 18. When the integer n is divided by 24, the remainder is 21. Which of the following must be a divisor of n ? • A . 3 • B . 4 • C . 5 • D . 6 • E . 9 PPS4-Set2 19. What is the value of the smallest positive integer n for which$$6^n$$is a multiple of 24 ? • A . 1 • B . 2 • C . 3 • D . 4 • E . 5 PPS4-Set2 20. If$$5^{x^{2}-2x}=\frac{1}{5}$$, what is the value of x ? • A . -1 • B . 1 • C .$$1+\sqrt{2}$$• D .$$1-\sqrt{2}$$• E .$$1+2\sqrt{2}$$Download PPS4-Set2 Quant Answers ## PPS4-Set3 PPS4-Set3 1. The price x of an item is increased 20 percent. Quantity A:80 percent of the price of the item after the increase Quantity B:x • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 2. AB and CD are line segments with endpoints on the circle with center O, and z>y. Quantity A:$$\frac{1}{2}$$the length of AB Quantity B:$$\frac{1}{2}$$the length of CD • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 3. n is a positive integer and 0< s< 10. Quantity A:$$\frac{1}{n}+\frac{1}{n+s}+\frac{1}{n+10}$$Quantity B:$$\frac{3}{n+10}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 4. In a list consisting of 10 numbers, 5 numbers are greater than 20 and 5 numbers are less than 20. Quantity A: The median of the numbers in the list Quantity B:20 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 5. The figure consists of two rectangles whose longer sides are all parallel to each other, and x=3. whose longer sides are all parallel to each other, and . Quantity A:The area of the shaded region Quantity B:The area of the smaller rectangle • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 6. x< 0< y Quantity A:$$\frac{|x|}{|y|}$$Quantity B:$$-\frac{x}{y}$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 7. Points R, S, and T are on the number line, and the distance between R and S is greater than the distance between S and T. Quantity A:RT Quantity B:RS • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set3 8. Jake, Mary, and Ito took a test in their history class. Jakes score of 68 was the lowest score in the class. Itos score of 85 was 5 less than Marys score. Mary had the highest score in the class. What was the range of all of the scores in the class? _____ PPS4-Set3 9. The driver of a car traveling at a speed of 40 miles per hour had to stop the car quickly. If the drivers reaction time was$$\frac{3}{4}$$of a second, approximately how many feet did the car travel during the driver`s reaction time? (1 mile = 5,280 feet) • A . 30 • B . 45 • C . 60 • D . 75 • E . 90 PPS4-Set3 10. Of the integers 2, 7, and 49, which, if any, are divisors of$$7^{49}+1$$? • A . None • B . 2 only • C . 7 only • D . 7 and 49 only • E . 2, 7, and 49 PPS4-Set3 11.$$a_{1},a_{2},...,a_{n},...$$In the sequence shown, the terms are defined by$$a_{n}=(2n-3)^2$$for all positive integers n. If the sum of the first k terms is 11, what is the value of k ? • A . 1 • B . 2 • C . 3 • D . 4 • E . 5 PPS4-Set3 12. A new car was sold with new brake linings that were each 0.250 inch thick. After the car had been driven 50,000 miles without replacing any brake linings, the thinnest brake lining was 0.085 inch thick. What was the percent decrease in the thickness of the thinnest brake lining? • A . 34% • B . 52% • C . 66% • D . 74% • E . 94% PPS4-Set3 13. Jena has a jar that contains 8 nickels and 12 dimes and no other coins. If she adds nickels to the jar one at a time until the ratio of the number of nickels to the total number of coins in the jar is 4 to 5, how many nickels must she add? • A . 20 • B . 24 • C . 32 • D . 40 • E . 56 PPS4-Set3 14. In 1994 the average annual salary of maintenance workers at Company X was approximately what percent of the average annual salary of maintenance workers nationwide in Country A ? • A . 25% • B . 75% • C . 90% • D . 110% • E . 120% PPS4-Set3 15. If Company X employed a total of 200 maintenance workers annually for the years 1991 through 1993 and a total of 150 maintenance workers annually for the years 1994 through 1997, what was the average amount of money spent annually by Company X on the salaries of its maintenance workers for the years 1991 through 1997 ? • A . 1,800,000 • B . 2,400,000 • C . 3,600,000 • D . 4,000,000 • E . 4,800,000 PPS4-Set3 16. For the years 1991 through 1997, what was the ratio of the range of the average annual salaries of maintenance workers at Company X to the range of those nationwide in Country A ? • A . 1 to 4 • B . 1 to 2 • C . 3 to 4 • D . 2 to 1 • E . 4 to 1 PPS4-Set3 17. In the xy-plane, the graph of y=(2x+3)(x-5) crosses the y-axis at the point (0,k). What is the value of k ? _____ PPS4-Set3 18. A, F, M, P, Y If the 5 letters listed above were randomly ordered, what is the probability that the resulting list would be either in alphabetical order (as shown) or in reverse alphabetical order? • A .$$\frac{1}{60}$$• B .$$\frac{1}{20}$$• C .$$\frac{1}{10}$$• D .$$\frac{1}{5}$$• E .$$\frac{2}{5}$$PPS4-Set3 19. When positive integer n is divided by 4, the remainder is 2. When n is divided by 3, the remainder is 1. Which of the following statements must be true? Indicate all such statements. • A . n≥10 • B . n is even. • C . n is divisible by 6. PPS4-Set3 20. In the xy-plane, line k and line p intersect at 90-degree angles. If the slope of line k is$$\frac{1}{2}$$, what is the slope of line p ? • A . -2 • B .$$-\frac{1}{2}$$• C . 0 • D .$$\frac{1}{2}$$• E . 2 Download PPS4-Set3 Quant Answers ## PPS4-Set4 PPS4-Set4 1. The figure shows a regular 9-sided polygon inscribed in a circle with center O. Quantity A: The perimeter of the regular polygon Quantity B:3 times the perimeter of triangle OAB • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 2. x>y Quantity A:xy Quantity B:$$x^2$$• A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 3. Set S consists of all possible values of the product ab, where a and b are integers such that 0< a< b < 10. Quantity A:The number of odd integers in S Quantity B:The number of even integers in S • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 4. n is a positive integer. Quantity A:The remainder when$$(n+7)^{2}-49$$is divided by n Quantity B:1 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 5. 450, 760, 900, 1,000, 1,250, 1,400, 1,750, 2,000 The eight amounts listed are the reported bonuses earned by eight employees during July. Two of the reported amounts are in error: one is 250 greater than the actual amount and one is 250 less than the actual amount. Quantity A:The standard deviation of the amounts of the eight reported bonuses Quantity B:The standard deviation of the amounts of the eight actual bonuses • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 6. The median of 5 different positive integers is 12. Quantity A: The least possible sum of the 5 integers Quantity B: 42 • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 7. 0 < w < x < y < z The average (arithmetic mean) of w, x, y, and z is less than the median of w, x, y, and z. Quantity A:z-y Quantity B:x-w • A . Quantity A is greater. • B . Quantity B is greater. • C . The two quantities are equal. • D . The relationship cannot be determined from the information given. PPS4-Set4 8. If the average (arithmetic mean) price of 3 items is 20 and the average price of 2 other items is 10, what is the average price of all 5 items? _____ PPS4-Set4 9. Sixty percent of the people who originally auditioned for parts in a musical were excused, and the rest were asked to audition again. Of those who were asked to audition again, 30 percent, or 18 people, were hired. How many people originally auditioned for parts? • A . 150 • B . 120 • C . 100 • D . 60 • E . 30 PPS4-Set4 10. r and n are integers such that r≥4 and n≥4. If (r-3)(n-3)<5, what is the greatest possible value of n ? • A . 4 • B . 5 • C . 6 • D . 7 • E . 8 PPS4-Set4 11. In the xy-plane shown, RS=TW. What is the value of k ? • A . 6.0 • B . 6.5 • C . 7.0 • D . 7.5 • E . 8.0 PPS4-Set4 12. The square region above has area 64 and is divided into six nonoverlapping triangular regions. If the area of triangular region A is 8, then the area of which of the following regions CANNOT be found? • A . B • B . C • C . A and B combined • D . C and D combined • E . B, E, and F combined PPS4-Set4 13. S is the set of all positive 3-digit integers. How many integers in S are multiples of both 7 and 13 ? • A . 6 • B . 9 • C . 12 • D . 15 • E . 18 PPS4-Set4 14. What is the number of Calories from protein in 1 serving of Brand K candy? • A . 0.5 • B . 1.0 • C . 2.0 • D . 4.0 • E . 8.0 PPS4-Set4 15. In 1 serving of Brand K candy, the ratio of the number of Calories from carbohydrates to the total number of Calories in the serving is closest to which of the following fractions? • A .$$\frac{1}{10}$$• B .$$\frac{1}{5}$$• C .$$\frac{3}{10}$$• D .$$\frac{2}{5}$$• E .$$\frac{3}{5}$$PPS4-Set4 16. A certain package of 4 brownies has 18 milligrams of cholesterol per brownie. The number of milligrams of cholesterol in the package of brownies is what percent less than the number of milligrams of cholesterol in 1 container of Brand K candy? • A . 40% • B . 50% • C . 67% • D . 75% • E . 80% PPS4-Set4 17. The manager of a small business took out two one-year loans, each for the same principal amount, to be repaid with interest at the end of the year. Loan S had a simple annual interest rate of 5 percent, and loan R had a simple annual interest rate of 6 percent. If the amount owed for loan S at the end of 9 months was 26,145, what was the amount owed for loan R at the end of 10 months? • A . 26,394 • B . 26,460 • C . 29,050 • D . 29,255 • E . 31,374 PPS4-Set4 18. A hardware store purchased x identical standard flashlights at 5 each and y identical deluxe flashlights at 7 each. The total cost to the store for both types of flashlights was 92. What is the ratio of x to y ? • A . 5 to 7 • B . 7 to 5 • C . 5 to 1 • D . 17 to 1 • E . It cannot be determined from the information given. PPS4-Set4 19. S:-3,3,-3,3,-3,3,... S is a sequence of integers in which -3 and 3 alternate, as shown. If the average (arithmetic mean) of the first n terms of S is$$-\frac{1}{5}, what is the value of n ?

n=_____
PPS4-Set4
20.

Data list I and data list II are summarized by boxplot I and boxplot II, respectively, as shown above. Which of the following statements must be true?

Indicate all such statements.
• A . The median of data list II is greater than the median of data list I.
• B . The range of data list I is greater than the range of data list II.
• C . The interquartile range of data list I is greater than the interquartile range of data list II.