GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #31 : Algebra

Solve for 

Possible Answers:

Correct answer:

Explanation:

Recall that 

With same base, we can write this equation: 

By subtracting  on both sides, 

 

Example Question #32 : Algebra

Solve for .

Possible Answers:

Correct answer:

Explanation:

Since  we can rewrite the expression.

With same base, let's set up an equation of .

By subtracting  on both sides, we get .

Take the square root of both sides we get BOTH  and 

Example Question #1 : Exponents And Rational Numbers

Solve for .

Possible Answers:

Correct answer:

Explanation:

They don't have the same base, however: .

Then . You would multiply the  and the  instead of adding.

Example Question #2 : Exponents And Rational Numbers

Solve for .

Possible Answers:

Correct answer:

Explanation:

There are two ways to go about this.

Method 

They don't have the same bases however: . Then 

You would multiply the  and the  instead of adding. We have 

Divide  on both sides to get .

 

Method :

We can change the base from  to 

 

This is the basic property of the product of power exponents. 

We have the same base so basically 

Example Question #10 : Exponents And Rational Numbers

Solve for .

Possible Answers:

Correct answer:

Explanation:

Since we can write 

With same base we can set up an equation of  

Divide both sides by  and we get 

Example Question #11 : Exponents And Rational Numbers

Solve for .

Possible Answers:

Correct answer:

Explanation:

 

We still don't have the same base however:  

Then,

.

With same base we can set up an equation of 

Divide both sides by  and we get 

Example Question #1 : How To Find A Rational Number From An Exponent

Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.

 

Quantity A             Quantity B

     43                              34 

Possible Answers:

Quantity A is greater.

The answer cannot be determined from the information given.

Quantity B is greater.

The two quantities are equal.

Correct answer:

Quantity B is greater.

Explanation:

In order to determine the relationship between the quantities, solve each quantity.

4is 4 * 4 * 4 = 64

34 is 3 * 3 * 3 * 3 = 81

Therefore, Quantity B is greater.

Example Question #31 : Algebra

Quantity A:

Quantity B:

Possible Answers:

The two quantities are equal.

The relationship cannot be determined from the information given. 

Quantity B is greater.

Quantity A is greater.

Correct answer:

Quantity B is greater.

Explanation:

(–1) 137= –1   

–1 < 0

(–1) odd # always equals –1.

(–1) even # always equals +1.

Example Question #31 : Algebra

 

Possible Answers:

Correct answer:

Explanation:

Anything raised to negative power means  over the base raised to the postive exponent. 

Example Question #12 : Exponents And Rational Numbers

Which of the following is not the same as the others?

Possible Answers:

Correct answer:

Explanation:

Let's all convert the bases to .

 This one may be intimidating but .

Therefore, 

 is not like the answers so this is the correct answer.

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