Quantitative Reasoning

Question 1

Jim has 10 apples and he gives 7 to Bill. Now, Bill has 3 times as many apples as Jim had. How many apples did Bill have to begin with?
A. 20
B. 17
C. 23
D. 2

Answer 1

C. 3 times Jim’s original amount is 3x10=30. This came after Jim gave 7 to Bill, so bill had to start with 23

Question 2

If f(x)=3x and g(x)=2x^2, what is g(f(-2))?
A. 24
B. -72
C. 48
D. 72

Answer 2

D. First evaluate f(-2):3(-2) = -6

Next evaluate g(-6):2(-6)^2 = 2(36)=72

Question 3

What is the value of i^2 x i^-3
A. 1
B. -i
C. 1/i
D. -1

Answer 3

C. Simplify the expression using the rules of exponents:

i^2 x i^-3 = i^2-3 = i^-1 = 1/i

Question 4

Which of the following is the same as log 85?
A. log 35 + log 50
B. In 1/85
C. log 255 - log 3
D. In 85

Answer 4

C. Recall the rules for condensing and expanding logarithms: log a + log b = log (a x b) and log a - log b = log (a/b)

Question 5

A man went to the store and bought pencils, pens, and erasers in the ration of 2:4:3. If he bought 6 erasers, how many items total did he buy?
A. 9
B. 18
C. 12
D. 10

Answer 5

B. The ratio can be expressed as 2x:4x:3x where 3x=6 represents the numbers of erasers bought. Solving for x: x=2, and plugging this value into the ratio: 2(2):4(2):3(2) —-> 4:8:6. Find the total number of items purchased by combining these numbers

Question 6

How many solutions does the equation have? 
(Long division 2+x) - x = 0
A. 3
B. 2
C. 1
D. 0

Answer 6

C. A solution to an equation is a value that when plugged in yields a true statement. Begin by isolating the square root and squaring both sides to eliminate it. Move all of the terms to one side and factor to solve for x

Question 7

The following are the results of a class test: 65, 75, 87, 86, 78, 92, 77, 81, 82, 86, 21, 91, 3. Which of the following is the best to use to quantify the overall performance on the exam?
A. Mean
B. Median
C. Mode
D. Standard Deviation

Answer 7

B. Since there are a few extreme outliers: 3 and 21, which differ from the norm, it is better to use the median, which is unaffected by outliers, rather than the mean, which is affected by outliers

Question 8

What is the x-intercept of y=e^5x + 2?
A. 2 
B. 0
C. ln2
D. no x-intercept

Answer 8

D. The x-intercept is where the function crosses the x-axis and can be found by setting the function equal to 0 and solving for x: 0=e^5x +2 —> -2=e^5x
To isolate the variable, take the natural log of both sides; however, ln -2 is undefined, so this function does not cross the x-axis

Question 9

What is 0.25% of 1/3?
A. 0.83
B. 0.083
C. 0.0083
D. 0.00083

Answer 9

D. Convert 0.25% to a fraction and multiply by 1/3. .25%= 25/10000 = 1/400 x 1/3 = 1/1200 = .00083