GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : Linear / Rational / Variable Equations

Quantity A: 

Quantity B: 11

Possible Answers:

The two quantities are equal.

Quantity A is greater

Quantity B is greater

The relationship cannot be determined.

Correct answer:

Quantity B is greater

Explanation:

Expand  out into .

Since , it can be seen that 

 so Quantity B is greater.

Example Question #11 : Equations / Inequalities

Quantity A: 

Quantity B: 

Possible Answers:

The two quantities are the same.

The relationship cannot be determined.

Quantity B is greater.

Quantity A is greater.

Correct answer:

Quantity A is greater.

Explanation:

To solve this problem, expand each function described by Quantities A and B:

Quantity A: 

Quantity B: 

Now note that Quantities A and B only differ in that Quantity A is greater by .

Since we are told that  is greater than  and thus always positive, Quantity A must be greater than Quantity B for all possible values of .

Example Question #12 : Equations / Inequalities

Quantity A: 

Quantity B: 

Possible Answers:

The relationship cannot be determined.

The two quantities are equal.

Quantity A is greater.

Quantity B is greater.

Correct answer:

Quantity A is greater.

Explanation:

Rather than manually finding common denominators and adding the fractions together, realize that

Since

Quantity A must be greater, and this can be seen without actually calculating its value.

Example Question #13 : Equations / Inequalities

Gre chart

Approximately, what was the percent growth of Beetleton's GDP from 2009 to 2010?

Possible Answers:

Correct answer:

Explanation:

Percent growth is given as:

For Beetleton, this can be expressed as (in terms of billions of US dollars):

Example Question #14 : Equations / Inequalities

The sum of two integers is . The larger integer is  greater than the smaller integer. What is the positive difference between the two?

Possible Answers:

Correct answer:

Explanation:

Let us write down what we are told in mathematical terms, designating the smaller integer as  and the larger integer as .

The sum of the two integers is :

And the larger integer is % greater than the smaller integer:

Writing the first equation in terms of  gives:

Which allows us to find :

Thus, the positive difference between the two is found as

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

 Rational_5

Possible Answers:

–1

–2

1

2

0

Correct answer:

2

Explanation:

Rational_2

Rational_3

Rational_4

Example Question #1 : How To Find The Solution To A Rational Equation With Lcd

Linesmb1

Possible Answers:

b/(m– 1)

–bm/(m+ 1)

bm/(m+ 1)

–b/(+ 1)

b/(m+ 1)

Correct answer:

b/(m+ 1)

Explanation:

Linesmb5

Linesmb4

Example Question #17 : Equations / Inequalities

In the equation below, , , and are non-zero numbers. What is the value of in terms of and ?

Possible Answers:

Correct answer:

Explanation:

Pkm_7-21-13

Pkm2_7-21-13

Example Question #18 : Equations / Inequalities

Four less than three times a certain number is equivalent to five plus four times this same number. What is three less than three times this number?

Possible Answers:

The answer cannot be determined from the information given.

Correct answer:

Explanation:

The key to solving this problem is deciphering the language and translating it into a numerical representation. The first part can be written as an equaltiy as follows:

Rearranging terms allows us to solve for this mystery number:

From there we can address the problem's question:

Example Question #19 : Equations / Inequalities

The arithmetic mean of , , , and  is 14.

Quantity A: 32

Quantity B: The arithmetic mean of  and 

Possible Answers:

Quantity B is greater.

Quantity A and Quantity B are equal.

Quantity A is greater.

The relationship between Quantity A and Quantity B cannot be determined.

Correct answer:

Quantity A and Quantity B are equal.

Explanation:

The definition of an arithmetic mean of a set of values is given as the sum of all the values divided by the total count of values:

Where   represents the  value in a set, and  is the number of values in the set.

Quantity B can thus be defined as follows:

Which simplifies to:

or, simplifying:

We are told that the mean of , and  is 14, which can be written as:

 

and then as 

Plugging this value into our definition of Quantity B, we can find its numerical value:

So 

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