GRE Math : Even / Odd Numbers

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #81 : Integers

If  and  are odd integers, and  is even, which of the following must be an odd integer?

Possible Answers:

Correct answer:

Explanation:

Even numbers come in the form 2x, and odd numbers come in the form (2x + 1), where x is an integer.  If this is confusing for you, simply plug in numbers such as 1, 2, 3, and 4 to find that:

Any odd number + any even number = odd number

Any odd number + any odd number = even number

Any even number x any number = even number

Any odd number x any odd number = odd number

a(b + c) = odd x (odd + even) = odd x (odd) = odd

Example Question #2 : Even / Odd Numbers

At a certain high school, everyone must take either Latin or Greek. There are  more students taking Latin than there are students taking Greek. If there are  students taking Greek, how many total students are there?

Possible Answers:

Correct answer:

Explanation:

If there are  students taking Greek, then there are  or  students taking Latin. However, the question asks how many total students there are in the school, so you must add these two values together to get:

 or  total students.

Example Question #82 : Integers

Assume  and  are both odd whole numbers and .

What is a possible solution for 

Possible Answers:

Correct answer:

Explanation:

An odd whole number minus an odd whole number will result in an even whole number. Since , the subtraction will result in a negative even whole number. The only answer that fits these requirements is .

Example Question #1 : How To Subtract Odd Numbers

Choose the answer below which best solves the following equation:

Possible Answers:

Correct answer:

Explanation:

If you have trouble with problems like this, try stacking the numbers, and subtracting one place at a time.  First, seven minus one is six, so that's your ones digit.  Next, three minus three is zero, so that's your tens digit.  Seven minus two is five, so that's your hundreds digit, and finally, one minus zero is one so that's you're thousands digit.  

Example Question #2 : How To Subtract Odd Numbers

Solve the following:

Possible Answers:

Correct answer:

Explanation:

To solve, simply subtract.  If you have trouble subtracting, try splitting the numbers up and adding your results:

 

Example Question #3 : How To Subtract Odd Numbers

Solve the following:

Possible Answers:

Correct answer:

Explanation:

To perform this operation, simply subtract.  If you are having trouble, you can split the problem into two easier to solve portions, by splitting the numbers up:

 

Example Question #4 : How To Subtract Odd Numbers

Solve the following:

Possible Answers:

Correct answer:

Explanation:

To solve, simply subtract.  If you have trouble subtracting, you can split the problem up and add your results back together:

Example Question #1 : How To Subtract Odd Numbers

Solve the following:

Possible Answers:

Correct answer:

Explanation:

To solve, simply subtract.  If you have trouble subtracting, you can split the numbers up, subtract, and add your results:

Example Question #1 : How To Divide Odd Numbers

What are three consecutive odd integers whose sum equals ?

Possible Answers:

Correct answer:

Explanation:

Set up the equation,

 .  

Simplify to  and solve for x to find .  

Therefore the 3 consecutive odd integrers are .

 

 

Example Question #2 : How To Divide Odd Numbers

Assume  and  are both odd whole numbers and .

What is a possible solution for ?

Possible Answers:

Correct answer:

Explanation:

The two requirements for this problem are that both  and  must be odd, and that . The only answer that fits both of these is . The other answers show either  or  is an even number.

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