OAT Study Prep - Quantitative reasoning

John receives a 15% raise, which increases his annual salary by $5,700. What was his yearly salary before the raise? a. $32,300 b. $35,000 c. $38,000 d. $43,700 e. $85,500

$38,000

A cell phone plan costs $30 per month and includes 500 min. Additional mins are charged at a rate of 8 cents per min. A total of 4% in taxes is added to the entire amount. If a customer uses 634 min, how much will the bill be that month? a. $10.72 b. $31.20 c. $40.72 d. $41.92 e. $42.35

$42.35

Which of the following is a point on the graph 3x - 2y = 4? a. (0,2) b. (1,4) c. (2,0) d. (2,1) e. (2,4)

(2,1)

If x^2 - 9 < 0, which of the following is true? a. x < -3 b. x > 3 c. x > 9 d. x < -3 or x > 3 e. -3 < x < 3

-3 < x < 3

In the month of December the average temperature was 40 degrees celsius. In the month of January, the average temperature fell 20% compared to the previous month, in the month of February the average temperature fell 20% compared to the previous month, in the month of March the average temperature rose 20% compared to the previous month, and in the month of April the average temperature rose 20% compared to the previous month. What was the average temperature in April? a. 37 degrees celsius b. 38 degrees celsius c. 39 degrees celsius d. 40 degrees celsius e. 41 degrees celsius

37 degrees celsius

There are twelve people on a basketball team. Three of them are left-handed, and six of them are taller than six feet. One of them is left-handed and taller than six-feet. How many people on the team are right-handed and less than six feet tall? a. 4 b. 5 c. 6 d. 7 e. 8

4

a man drove 50 miles from city A due north to city B then turned due west and drove 120 miles to city C. How many more miles did the man drive than he would have if he had driven straight to city A from C? a. 40 miles b. 90 miles c. 130 miles d. 170 miles e. 180 miles

40 miles a^2 + b^2 = c^2

A riding lawn mower can mow an acre of lawn in 20 min. A standard lawn mower can mow half of an acre in 30 min. How long will it take to mow 3 acres if both lawn mowers are working together? a. 15 min b. 20 min c. 30 min d. 45 min e. 60 min

45 min

Oak trees line both sides of a street for a length of 375 meters. If there is 16 meters of space between the trees and each tree is 1 meter wide, how many trees are there along the street? a. 42 b. 44 c. 46 d. 50 e. 64

46

a factory cut its labor force by 16%, but then increased it by 25% of the new amount. What was the net percent change in the size of the workforce? a. no net change b. 3% increase c. 5% increase d. 9% increase c. 10% increase

5% increase

An alloy of tin and copper has 6 lbs of copper for every 2 lbs of tin. If 200 lbs of the one alloy are made, how many pounds of tin are required? a. 25 b. 50 c. 100 d. 125 e. 150

50 1/4 (200)

a 25 ounce solution is 20% alcohol. If 50 ounces of water were added to it, what % of the new solution is alcohol? a. 5% b. 6.67% c. 8.5% d. 10% e. 20%

6.67%

What is 15% of 50% of (4/5)^2? a. 2/75 b. 6/125 c. 9/105 d. 11/95 e. 17/87

6/125

A train must travel a straight-line path of 685 miles in 10 hrs. If during the first 7 hrs the train travels at an average speed of 70 mph, what must the trains average speed be, in mph, for the remaining 3 hrs? a. 58 b. 64 c. 65 d. 67 e. 68

65 rate = distance / time

A wire is cut into three equal parts. The resulting segments are then cut into 4, 6, and 8 equal parts, respectively. If the length of each of the resulting segments is an integer, what is the shortest possible length of the original wire? a. 24 b. 36 c. 48 d. 54 e. 72

72

An instructor gives 5 exams for the semester. If a student had an average (arithmetic mean) score of 87 for the first 4 exams during the semester and an average (arithmetic mean) score of 84 for all 5 exams, what score did the student receive on the 5th exam? a. 72 b. 75 c. 78 d. 80 e. 81

72

For how many positive integers x is (130 / x) an integer? a. 8 b. 7 c. 6 d. 5 e. 3

8

A motorist travels 90 miles at the rate of 20 miles per hour. If the same motorist returns the same distance at a rate of 40 miles per hour, what is the average speed for the entire trip, in miles per hour? a. 20 b. 65/3 c. 80/3 d. 30 e. 130/3

80/3 time = distance / rate

The scores for student A are normally distribute about an average (arithmetic mean) of 85 with a standard deviation of 5. The scores for students B are normally distributed about an average (arithmetic mean) of 90 with a standard deviation of 2. Quantity A: the probability that student A gets a 95 on the next test Quantity B: the probability that student B gets 95 on the next test 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

Quantity A is greater

A video game charges 15 dollars / month for play time, and an additional $1.50 per luxury item purchased in a game. If Jenny spent $45 in the time she played the game, how much of that money went towards luxury items? 1. Jenny played the game for 2 months 2. Jenny bought 10 luxury items a. Statement 1 by itself is sufficient to answer the question, but statement 2 by itself is not b. Statement 2 by itself is sufficient to answer the question, but statement 1 by itself is not c. Statements 1 and 2 taken together are sufficient to answer the question, even though neither statement by itself is sufficient d. either statement by itself is sufficient to answer the question e. Statements 1 and 2 taken together are not sufficient to answer the question, requiring more date pertaining to the problem

either statement by itself is sufficient to answer the question

What is the average (arithmetic mean) of n, n + 1, n +2, and n +3? a. n b. n + 1 c. n + 1.5 d. n = 2 e. n + 6

n + 1.5

The cos 45 degrees is equivalent to a. sin 90 degrees b. sin 45 degrees c. tan 90 degrees d. cos 90 degrees e. tan 45 degrees

sin 45 degrees

If x, y, and z are all positive and (0.04)x = 5y = 2z, then which of the following is true? a. x < y < z b. x < z < y c. y < x < z d. y < z < x e. z < y < x

y < z < x

If snow falls at a rate of x feet per minute, how many hours would it take for y feet to fall? a. x/60y b. y/60x c. 60x/y d. 60y/x e. 60xy

y/60x rate x time = amount of snowfall

If one pint of milk with 2% fat is added to half a pint of cream with 50% fat, what is the percentage of fat in the mixture? a. 12 b. 13.5 c. 18 d. 26 e. 27

18

What is 1/5 of (225)^1.2? a. 3 b. 7 c. 15 d. 22.5 e. 25

3

what is the value of |5-31| + |8-4| / 5|4+(-2)|? a. -2 1/5 b. 2 c. 2 1/5 d. 3 e. 6

3

At a sporting event, home team fans outnumber away team fans 10:1. If the stadium holds 35,000 total fans, how many away fans are at the game? a. 3,182 b. 3,500 c. 6,417 d. 31,500 e. 32,083

3,182

Which of the following is not equal to 0.0675? a. 67.5 x 10^-3 b. 6.75 x 10^-2 c. 0.675 x 10^-2 d. 0.00675 x 10^2 e. 0.0000675 x 10^3

0.00675 x 10^2

Which of the following is less than 1/6? a. 0.1666 b. 3/18 c. 0.167 d. 0.1667 e. 8/47

0.1666

If 2/(3b) = 12c, what is the value of b in terms of c? a. 1/(36c) b. 1/(18c) c. 8c d. 18c e. 36c

1/(18c)

What is the value of x if x > 0 and x^2 /3 = x/81 a. 1/81 b. 1/27 c. 1/9 d. 27 e. 81

1/27

Which of the following is equal to a/b if 14a = 1/3b? a. 1/42 b. 1/14 c. 14 d. 3/14 e. 42

1/42

What is 27% of (5.0 x (2.0)^3)? a. 3.1 b. 5.9 c. 10.8 d. 16.4 e. 19.6

10.8

A man drives 18 miles from city A due north to city b, then turns due east and drives 24 miles to city c. How many more miles did the the man drive taking this route than he would have if he had driven straight to City A from C? a. 6 miles b. 11 miles c. 12 miles d. 24 miles e. 30 miles

12 miles a2 + b2 = c2

If 3x + 2y = 6 and 4x - 3y = 4, what is the value of y? a. 26/17 b. 12/17 c. 8/17 d. 2/17 e. -26/17

12/17

A class of 40 students is to be divided into smaller groups. If each group is to contain 3,4, or 5 people, what is the largest number of groups possible? a. 8 b. 10 c. 12 d. 13 e. 14

13