GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #1 : How To Subtract Odd Numbers

Assume \displaystyle m and \displaystyle n are both odd whole numbers and \displaystyle m< n.

What is a possible solution for \displaystyle m-n?

Possible Answers:

\displaystyle 0

\displaystyle 3

\displaystyle 6

\displaystyle -12

Correct answer:

\displaystyle -12

Explanation:

An odd whole number minus an odd whole number will result in an even whole number. Since \displaystyle m< n, the subtraction will result in a negative even whole number. The only answer that fits these requirements is \displaystyle -12.

Example Question #2 : How To Subtract Odd Numbers

Choose the answer below which best solves the following equation:

\displaystyle 1737 - 231 =

Possible Answers:

\displaystyle 1308

\displaystyle 1606

\displaystyle 1507

\displaystyle 1407

\displaystyle 1506

Correct answer:

\displaystyle 1506

Explanation:

\displaystyle 1737 - 231 = 1506

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 #3 : How To Subtract Odd Numbers

Solve the following:

\displaystyle 1211 - 387 =

Possible Answers:

\displaystyle 844

\displaystyle 825

\displaystyle 832

\displaystyle 829

\displaystyle 824

Correct answer:

\displaystyle 824

Explanation:

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

\displaystyle 1211 - 387 =

\displaystyle (1200 - 380) + (11 - 7) =

\displaystyle 820 + 4 =

\displaystyle 824

 

Example Question #4 : How To Subtract Odd Numbers

Solve the following:

\displaystyle 35 - 17 =

Possible Answers:

\displaystyle 15

\displaystyle 16

\displaystyle 18

\displaystyle 9

\displaystyle 17

Correct answer:

\displaystyle 18

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:

\displaystyle 35 - 17 =

\displaystyle (20-10)+(15 - 7) =

\displaystyle 10 + 7 =

\displaystyle 17 

Example Question #5 : How To Subtract Odd Numbers

Solve the following:

\displaystyle 133 - 35 =

Possible Answers:

\displaystyle 85

\displaystyle 99

\displaystyle 98

\displaystyle 97

\displaystyle 87

Correct answer:

\displaystyle 98

Explanation:

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

\displaystyle 133 - 35 =

\displaystyle (120 - 30) + (13 -5) =

\displaystyle 90 + 8 =

\displaystyle 98

Example Question #6 : How To Subtract Odd Numbers

Solve the following:

\displaystyle 333 - 121 =

Possible Answers:

\displaystyle 192

\displaystyle 212

\displaystyle 232

\displaystyle 242

\displaystyle 222

Correct answer:

\displaystyle 212

Explanation:

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

\displaystyle 333 - 121 =

\displaystyle (300 - 100) + (33-21) =

\displaystyle 200 + 12 =

\displaystyle 212

Example Question #11 : Even / Odd Numbers

What are three consecutive odd integers whose sum equals \displaystyle 57?

Possible Answers:

\displaystyle 19,21,23

\displaystyle 15,17,19

\displaystyle 17,19,21

\displaystyle 15,17,23

Correct answer:

\displaystyle 17,19,21

Explanation:

Set up the equation,

 \displaystyle (x)+(x+2)+(x+4)= 57.  

Simplify to \displaystyle 3x+6=57 and solve for x to find \displaystyle x=17.  

Therefore the 3 consecutive odd integrers are \displaystyle 17,(17+2),\& (17+4)= 17,19,21.

 

 

Example Question #2 : How To Divide Odd Numbers

Assume \displaystyle a and \displaystyle b are both odd whole numbers and \displaystyle a>b.

What is a possible solution for \displaystyle \frac{a}{b}?

Possible Answers:

\displaystyle 2

\displaystyle \frac{1}{2}

\displaystyle \frac{13}{3}

\displaystyle \frac{3}{13}

Correct answer:

\displaystyle \frac{13}{3}

Explanation:

The two requirements for this problem are that both \displaystyle a and \displaystyle b must be odd, and that \displaystyle a>b. The only answer that fits both of these is \displaystyle \frac{13}{3}. The other answers show either \displaystyle b< a or \displaystyle a is an even number.

Example Question #161 : Arithmetic

Solve for \displaystyle a:

\displaystyle 31a = 279

Possible Answers:

\displaystyle a=4

\displaystyle a = 9

\displaystyle a = 11

\displaystyle a = 8

\displaystyle a = 7

Correct answer:

\displaystyle a = 9

Explanation:

To solve, divide both sides of the equation by \displaystyle 31:

\displaystyle 31a = 279

\displaystyle a=279/31

\displaystyle a = 9

As a check, if you divide an odd number by another odd number, your result should be odd. 

Example Question #162 : Arithmetic

Solve for \displaystyle b:

\displaystyle 121b = 1331

Possible Answers:

\displaystyle b=3

\displaystyle b = 13

\displaystyle b = 12

\displaystyle b = 11

\displaystyle b = 10

Correct answer:

\displaystyle b = 11

Explanation:

To solve, isolate your variable by dividing both sides of the equation by \displaystyle 121:

\displaystyle 121b = 1331

\displaystyle b = 1331/121

\displaystyle b = 11

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