GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #2 : How To Multiply Even Numbers

Which of the following integers has an even integer value for all positive integers  and ?

Possible Answers:

Correct answer:

Explanation:

There are certain patterns that can be used to predict whether the product or sum of numbers will be odd or even. The sum of two odd numbers is always even, as is the sum of two even numbers. The sum of an odd number and an even number is always odd. In multiplication the product of two odd numbers is always odd. While the product of even numbers, as well as the product of odd numbers multiplied by even numbers is always even. So for this problem we need to find scenarios where the only possibile answers are even.  can only result in even numbers no matter what positive integers are used for  and , because  must can only result in even products; the same can be said for . The rules provide that the sum of two even numbers is even, so  is the answer.

Example Question #1 : How To Divide Even Numbers

Choose the answer below which best solves the following equation:

Possible Answers:

Correct answer:

Explanation:

To solve this problem, set up long division for yourself.  First, you know that your hundreds digit of the solution will be one, as twelve goes into seventeen one time.  Then, you take twelve away from seventeen, and are left with three remaining.  Bring down your next digit over from the dividend, and you are left with thirty two, which twelve goes into four times.  Already, you know that the answer has to be  as none of the other answers fit the correct pattern.

Example Question #1 : How To Divide Even Numbers

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve, first isolate the variable by dividing both sides of the equation by :

As a check, know that any time you divide an even number by another even number, you will get an even result. 

Example Question #172 : Arithmetic

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve, isolate your variable by dividing both sides of the equation by :

As a check, know that any time you divide an even number by another even number, the result will be even. 

Example Question #171 : Arithmetic

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve, isolate the variable by dividing both sides of the equation by :

As a check, know that any time you divide an even number by another even number, the result will be even.  

Example Question #4 : How To Divide Even Numbers

Solve for :

Possible Answers:

Correct answer:

Explanation:

To solve, isolate the variable by dividing both sides of your equation by :

As a check, know that any time you divide an even number by another even number, your result will be even. 

Example Question #111 : Integers

Assume  and  are both even whole numbers and .

What is a possible solution of ?

Possible Answers:

Correct answer:

Explanation:

Since , then the final answer will be a number greater than one. The only answer that fits is .

Example Question #1 : How To Find The Missing Number In A Set

The product of two integers is 14. Which of the following could be the average of the two numbers?  

Possible Answers:

\dpi{100} \small 5.5

\dpi{100} \small -6.5

\dpi{100} \small -5.5

\dpi{100} \small -4.5

\dpi{100} \small 3.5

Correct answer:

\dpi{100} \small -4.5

Explanation:

The two integers in this case, and their respective averages, could be:

 Only \dpi{100} \small -4.5 is one of the answer choices. 

 

Example Question #1 : How To Find The Missing Number In A Set

Which of these is a natural number?

Possible Answers:

All of these are natural numbers.

None of these are natural numbers .

Correct answer:

Explanation:

The natural numbers are the positive integers (whole numbers) starting with 1. 

Example Question #2 : Sets

Which of the following pairs of events are mutually exclusive?

Possible Answers:

 for all  values, the numbers greater than

the even numbers, the numbers greater than

the negative numbers,

the positive numbers, the numbers less than

the numbers less than , the numbers greater than

Correct answer:

the positive numbers, the numbers less than

Explanation:

We can think of mutually exclusive in terms of a Venn diagram.  We are looking for the pair of events that has nothing in common.  The only sets that don't have a single number in common are the positive numbers and the numbers less than –200. 

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