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Example Questions
Example Question #1 : Evaluating Expressions
Quantitative Comparison
0 < x < 1
A
---
(2x + 5)/(x2)
B
---
5x
The relationship cannot be determined from the information given
Quantity B is greater
Quantity A is greater
The two quantities are equal
Quantity A is greater
Since A is a fraction with an exponential term in the denominator, its maximum value is when x is at a minimum. In B, the maximum value is when x approaches its maximum. Therefore, we can check whether there is overlap between the two quantities: No matter how close to either 0 or 1 x reaches, A will always be greater than B. (In fact, the minimum value for A is ~7, while the maximum value of B is ~5)
Be sure to keep your value of x consistent when plugging between the two fractions! The question asks for when they have the same x-value, not for when they are solved independently.
Example Question #2 : Evaluating Expressions
If x = -4 and y = 7, what is the value of 3x-5y?
Substitute the values into equation: 3(-4) - 5(7) = -12 - 35 = -47.
Example Question #1 : Evaluating Expressions
Quantitative Comparison
Quantity A: x
Quantity B: 2x
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
The relationship cannot be determined from the information given.
For a quantitative comparison question such as this one, it is best to first plug in the numbers 0, 1, and –1. Plugging in 0 gets the same answer for both columns. Plugging in 1 makes Quantity B bigger. Plugging in –1 makes Quantity A bigger. Therefore the answer cannot be determined.
Example Question #241 : Equations / Inequalities
A store sells 17 coffee mugs for $169. Some of the mugs are $12 each and some are $7 each. How many $7 coffee mugs were sold?
6
10
7
8
9
7
The answer is 7.
Write two independent equations that represent the problem.
x + y = 17 and 12x + 7y = 169
If we solve the first equation for x, we get x = 17 – y and we can plug this into the second equation.
12(17 – y) + 7y = 169
204 – 12y + 7y =169
–5y = –35
y = 7
Example Question #1 : How To Evaluate Algebraic Expressions
Kim has 22 coins made up of quarters, nickles, and dimes that total $2.45. Kim has twice as many nickles as quarters. How many dimes does she have?
12
5
Cannot be determined
7
10
7
The answer is 7.
Let us first write down three equations that represent the problem:
n + d + q = 22
2q = n
5n + 10d + 25q = 245
Lets plug the second equation into the first and third equations:
(2q) + d + q = 22
5(2q) + 10d + 25q = 245
Solve the first equation for d and plug into the last equation:
d = 22 – 3q
10q + 10(22 – 3q) + 25q = 245
Solve for q.
220 – 30q + 25q + 10q = 245
5q = 25
q = 5
Therefore, n = 10 and d = 7
Example Question #1 : How To Evaluate Algebraic Expressions
In the equation ax + b = 32, x is a constant. If a = 3 when b = 2, what is a when b = 12?
13
2
3
7
10
2
The answer is 2.
First solve for the constant x:
3x + 2 = 32
x = 10
Now plug in x = 10 and b = 12:
a(10) + 12 = 32
a = 2
Example Question #41 : Expressions
A specialty socket wrench, typically priced at $29.99, is on sale for 30% off. An additional 45% is discounted at the register. What is the final sale price of the wrench?
$22.49
$11.55
$7.50
$4.05
$4.95
$11.55
The answer is $11.55
The original cost is $29.99 but we are going to discount 30%, meaning we will only pay 70%. The new prices is 29.99 x 0.70 = $20.99.
The new price is then dicounted an additional 45%, meaning we will only pay 55% of the new price. The final price is 20.99 x 0.55 = $11.55.
Example Question #2 : How To Evaluate Algebraic Expressions
Quantitative Comparison
x is an integer.
Quantity A: (x + 1)2
Quantity B: (x – 1)2
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
When picking numbers, we should always try to plug in the numbers 0, 1, and –1 first.
First try 0:
(0 + 1)2 = 1
(0 – 1)2 = 1
Here the two quantities are equal.
Now try 1:
(1 + 1)2 = 4
(1 – 1)2 = 0.
Here Quantity A is greater.
Therefore the relationship cannot be determined.
Example Question #9 : Evaluating Expressions
Barry's workout today consists of 10 squats every minute on the minute and 6 situps every other minute for 1 hour. How many squats and situps does Barry do in total?
800
1200
1000
960
780
780
squats: 10 squats * 60 minutes = 600 squats
situps: 6 situps * 30 minutes = 180 situps
total = 600 + 180 = 780
Example Question #10 : Evaluating Expressions
Let and
be integers such that
and
.
Quantity A Quantity B
0
The relationship cannot be determined from the information given
Quantity A is greater
Quantity B is greater
Quantity A and Quantity B are equal
The relationship cannot be determined from the information given
The quantity produces a minimum of
and a maximum of 4, which are less than and greater than 0, respectively. Therefore, the answer cannot be determined from the information given.
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