### All GRE Math Resources

## Example Questions

### Example Question #1 : How To Evaluate Algebraic Expressions

Quantitative Comparison

0 < x < 1

A

---

(2x + 5)/(x^{2})

B

---

5x

**Possible Answers:**

Quantity B is greater

The relationship cannot be determined from the information given

The two quantities are equal

Quantity A is greater

**Correct answer:**

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 #1 : How To Evaluate Algebraic Expressions

If x = -4 and y = 7, what is the value of 3x-5y?

**Possible Answers:**

**Correct answer:**-47

Substitute the values into equation: 3(-4) - 5(7) = -12 - 35 = -47.

### Example Question #1 : How To Evaluate Algebraic Expressions

Quantitative Comparison

Quantity A: *x*

Quantity B: 2*x*

**Possible Answers:**

Quantity A is greater.

Quantity B is greater.

The relationship cannot be determined from the information given.

The two quantities are equal.

**Correct answer:**

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 #2011 : Act Math

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?

**Possible Answers:**

10

8

9

7

6

**Correct answer:**

7

The answer is 7.

Write two independent equations that represent the problem.

*x* + *y* = 17 and 12*x* + 7*y* = 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*) + 7*y* = 169

204 – 12*y* + 7*y* =169

–5*y* = –35

*y* = 7

### Example Question #41 : 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?

**Possible Answers:**

5

10

12

7

Cannot be determined

**Correct answer:**

7

The answer is 7.

Let us first write down three equations that represent the problem:

*n* + *d* + *q* = 22

2*q* = *n*

5*n* + 10*d* + 25*q* = 245

Lets plug the second equation into the first and third equations:

(2*q)* + *d* + *q* = 22

5(2*q*) + 10*d* + 25*q* = 245

Solve the first equation for *d* and plug into the last equation:

*d* = 22 – 3*q*

10q + 10(22 – 3*q*) + 25*q* = 245

Solve for *q*.

220 – 30*q* + 25*q* + 10*q* = 245

5*q* = 25

*q* = 5

Therefore, *n* = 10 and *d* = 7

### Example Question #1 : Evaluating Expressions

In the equation *ax* + *b* = 32, *x* is a constant. If *a* = 3 when *b* = 2, what is *a* when *b* = 12?

**Possible Answers:**

7

3

2

13

10

**Correct answer:**

2

The answer is 2.

First solve for the constant *x:*

3*x* + 2 = 32

*x* = 10

Now plug in *x* = 10 and *b* = 12:

*a*(10) + 12 = 32

*a* = 2

### Example Question #1 : How To Evaluate Algebraic 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?

**Possible Answers:**

$11.55

$22.49

$4.95

$7.50

$4.05

**Correct answer:**

$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 #1 : How To Evaluate Algebraic Expressions

Quantitative Comparison

*x* is an integer.

Quantity A: (x + 1)^{2}

Quantity B: (x – 1)^{2}

**Possible Answers:**

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

**Correct answer:**

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 : How To Evaluate Algebraic 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?

**Possible Answers:**

1200

1000

960

800

780

**Correct answer:**

780

squats: 10 squats * 60 minutes = 600 squats

situps: 6 situps * 30 minutes = 180 situps

total = 600 + 180 = 780

### Example Question #10 : How To Evaluate Algebraic Expressions

Let and be integers such that and .

Quantity A Quantity B

0

**Possible Answers:**

The relationship cannot be determined from the information given

Quantity A and Quantity B are equal

Quantity A is greater

Quantity B is greater

**Correct answer:**

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.