Test 1 (Quantitative Reasoning)

What is the volume of a cylinder

πr^2h

A square has sides of length X. If circles are centered on each of the corners of the square such that two have radii of (1/4)X and two have radii of (1/2)X, what proportions of the area of the square is also covered by a circle? A. (3π/32) B. (5π/32) C. (8/5π) D. (3π/8) E. (5π/8)

(5π/32)

What is the value of Y if -7X + 5Y = 1 and X - Y = 3? A. -11 B. -9 C. -8 D. 8 E. 11

-11

Which of the following is equal to 247 X 763 - 1,763 X 247? A. -17,630 B. -24,700 C. -176,300 D. -188,461 E. -247,000

-247,000

cos 60°

1/2

sin 30°

1/2

If sqrt[(1/X)-1] = 7, then X = ? A. 1/64 B. 1/50 C. 1/8 D. sqrt(1/6) E. 48

1/50

A carnival game has 9 ducks that pop up at random out of a set of holes. One duck pops up at a time and returns into its hole before the next comes out. There are 4 blue ducks, 3 red ducks, 1 brown duck, and 1 gold duck. In order to win, the gamer needs to knock down the gold duck. What is the probability that the gold duck will be the third duck to pop up? A. 1/729 B. 1/120 C. 1/81 D. 1/27 E. 1/9

1/9

A drawer contains 4 red and 8 black pens. what is the probability that a person randomly grabbing two pens at once will grab two black pens? A. 14/36 B. 14/33 C. 4/9 D. 4/8 E. 3/4

14/33

Which of the following fractions is largest? A. 73/200 B. 5/8 C. 17/19 D. 1/2 E. 75/100

17/19

If sin A = 1/sqrt(5), which of the following is the value of Cos A? [0<A<π/2) A. 1/sqrt(5) B. 2/sqrt(5) C. 1/5 D. 1/sqrt(5) E. 2/5

2/sqrt(5)

Y + 8 is what percent of (Y^3)-4, when Y = 4? A. 20 B. 25 C. 33(1/3) D. 300 E. 500

20

For new car purchases, an automobile company allows the selection of two free "extras" from a list of seven. How many different ways can a car be customized with extras? A. 21 B. 28 C. 35 D. 42 E. 49

21

Five integers are listed in order from least to greatest. Beginning with the second integer in the list, each subsequent integer is 4 greater than the previous integer. If the sum of the five integers is 165, what is the first integer? A. 21 B. 25 C. 29 D. 33 E. 35

25

What is the distance between (-6,7) and (4,31)? A. 10 B. 18 C. 24 D. 26 E. 37

26

What is the formula for perimeter of a circle

2πr

What is the area of a cylinder

2πrh+2πr^2

Which of the following contains all the solutions and only the solutions of the equation sqrt[(4X^2)+28] = 2X+2? A. 3 B. -2,2 C. 2,3 D. 2sqrt(6), -2sqrt(6) E. 3,8

3

A circular indoor track has an outer radius of 100ft. It consists of an outer running lane 10 ft wide and an inner walking lane 5 feet wide. Approximately what percent of the total lane area is occupied by the walking lane? A. 13 B. 32 C. 33 D. 46 E. 49

32

Eight times a number equals 35 more than the number. What is the number? A. 3 B. 4 C. 5 D. 6 E. 7

5

A/2 is what percent of A^2/3, when A = 3? A. 25 B. 33(1/3) C. 50 D. 66(2/3) E. 75

50

One hose can fill a pool in 2 hours and another hose can fill the pool in 3 hours. How many hours does it take both hoses operating at the same time to fill the pool? A. 2/3 B. 5/6 C. 6/5 D. 4/3 E. 7/4

6/5

If (3/8)Y - Y > (7/8) - (Y/8), which of the following must be true? A. Y < -7/4 B. Y < -15/4 C. Y < -15/2 D. Y < 15/2 E. Y > -15/4

Y < -7/4

If [(X^2)-8][X + 7] < 0, then what are all the possible ranges of X? A. X < -7 B. X < 2sqrt(2) C. -7 < X < 2sqrt(2) D. -2sqrt(2) < X < 2sqrt(2) E. X < -7, or -2sqrt(2) < X < 2sqrt(2)

X < -7, or -2sqrt(2) < X < 2sqrt(2)

If Y = (5X + 2)/(X-6), then which of the following gives X in terms of Y for all values of Y where the expression for X in terms of Y is defined? A. X = (2+6Y)/(5-Y) B. X = 6Y/(Y-5) C. X = (2+6Y)/(Y+5) D. X = (2-6Y)/(Y-5) E. X = (2+6Y)/(Y-5)

X = (2+6Y)/(Y-5)

For which of the following sets of values is the mean greater than the median? A. [2,2,8,9,13] B. [3,6,7,10,12] C. [4,4,4,4,4] D. [6,7,8,8,9] E. [5,8,27,33]

[3,6,7,10,12]

If C = (3P+3)/(2P-2), then which of the following represents P? A. [C+(3/2)]/[C-(3/2)] B. [C-(3/2)]/[C+(3/2)] C. 2C/3 D. 3(C+1)/2(C-1) E. 2[C-(2/3)]/C

[C+(3/2)]/[C-(3/2)]

What is the distance formula?

d = √[(X2 - X1)^2 + (Y2 - Y1)^2]

What is the diameter of a circle whose perimeter intersects the four corners of a square with a perimeter of 4? A. 1/sqrt(2) B. 1 C. sqrt(2) D. 2 E. 2sqrt(2)

sqrt(2)

Line L contains points (-1,3) and (4,-2). Which of the following is an equation of line L? A. y= x + 4 B. y + x = 2 C. y + x = 3 D. y - x = 1 E. y = -x - 3

y + x = 2

What is the formula for area of a circle

πr2

If r and s are positive integers and 4r + 6s is equal to 3a + 2s, then which of the following is equal to 2s? A. -2r+(3/2)a B. -4r+3d C. -r+(3/4)a D. r-(3/4)a E. (4/3)r+3a

-2r+(3/2)a

If the expression: (X^2 + 6)(-5 - X)(X + 8)/ sqrt(X^2 + 1) is positive, which of the following could be the value of X? A. -7 B. -1 C. 5 D. 6 E. 8

-7

If X > 0, what is the value of the expression (I-XI + I2XI)/I-3XI? A. -1 B. -1/3 C. 1/3 D. 1 E. 3X

1

In the right triangle ABC with right angle at A, BC = 5, and AC = 2√6. What is the length of AB? A. 1 B. √49 C. 3√6 D. 7√6 E. 75

1

What is the value of sqrt(.49)/.7? A. .7 B. sqrt(.7) C. 1 D. 2 E. sqrt(7)

1

In a right triangle, the angle∠ADC = 60, and DC = 22. Which of the following is the length of the line segment AD? A. 10 B. 11 C. sqrt(130) D. 10sqrt(3) E. 11sqrt(3)

11

Which of the following is equal to sin 7π/8? A. sin 3π/4 B. sin π/8 C. sin π/4 D. cos π/8 E. cos 7π/8

sin π/8

Sherry invests money in stock. Her initial investment is $3,000, and after one month the stock's value increases by 20%. After another month, her investment's value dips by 10%. In the third month, her stock's value increases again, by 15%. How much is her investment worth now? A. $3,100 B. $3,726 C. $3,240 D. $3,750 E. $4,350

$3,726

What is 75% of (42 - 4^2)? A. 18.4 B. 19.5 C. 20.2 D. 21.3 E. 22.5

19.5

A car loses half its value every 3 years. If 6 years after it was made it is worth $12,000 less than its original value, how many dollars will it be worth 9 years after it was made? A. 1,000 B. 2,000 C. 3,000 D. 4,000 E. 6,000

2,000

Which of the following is equal to the value of 115% of 95% of 20? A. 21 B. 21.85 C. 22 D. 40.85 E. 42

21.85

What is the maximum number of isosceles right triangles whose legs are 3 inches long that can be cut from a rectangular sheet of paper measuring 14 X 10 inches? A. 12 B. 15 C. 24 D. 30 E. 31

24

What is the maximum possible straight-line distance between two points on the surface of a solid with dimensions 4 x 2 x 2? A. sqrt(5) B. 4 C. 2sqrt(5) D. 2sqrt(6) E. 8

2sqrt(6)

What is the distance on a conventional two-dimensional graph between the coordinates (-5,7) and (3,-1)? A. 4 B. 6 C. 2sqrt(10) D. 8 E. 8sqrt(2)

8sqrt(2)

An 8-sided carousel has one horse on each vertex. 3 of the horses are red, 3 are blue, and 2 are green. A child is stationary in front of one vertex while waiting to ride and waits for three rounds. For each round, the carousel turns a random number of times before stopping with one vertex directly in front of the child. What are the chances that the carousel will stop with a green horse in front of the child on the first turn, a red horse in front of the child on the second turn, and a blue horse in front of the child on the last round? A. 6/ 336 B. 3/225 C. 3/128 D. 9/256 E. 9/100

9/256

What is the height of a cylinder with radius 3sqrt(13) and volume 117sqrt(13)? A. √ 13/π B. √ 13/3 C. √ 13/2 D. √ 13 E. √ 26

√ 13/π

cos 45°

√2/2

sin 45°

√2/2

cos 30°

√3/2

sin 60°

√3/2