GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #1 : How To Graph An Inequality With A Number Line

Numberline1

$A: y^2 <\frac{x}{2}$

B: y>-x

$C: \frac{x}{y}>-1$

Which of the following is true?

Possible Answers:

$\textup{B only.}$

$\textup{B and C.}$

$\textup{A only.}$

$\textup{A and C.}$

$\textup{C only.}$

Correct answer:

$\textup{B only.}$

Explanation:

Since is always positive, and |x|>|y| , it follows that y>-x for all possible values.

For the A, it is possible to choose values that make the statement false, for example y=-0.9 and x=1.1 .

C is always false.

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Example Question #124 : Arithmetic

Numberline2

A: |y+x|>2x

B:(x+y)^2>0

C:x^y>0

Which of the statements is always true?

Possible Answers:

$\textup{A and C}$

$\textup{B only}$

$\textup{A only}$

$\textup{A and B}$

$\textup{C only}$

Correct answer:

$\textup{C only}$

Explanation:

Although C may approach zero for large values of |y| and values of x>1 , it will never actually reach it for real values.

A and B, however, have x and y values which make them false:

For A, an example is y=-100,x=1

For B, |y|=x would make the value zero.

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Example Question #562 : Arithmetic

2x + 6 > 16

Which of the following is a graph for the values of defined by the inequality stated above?

Possible Answers:

Ineq14

Ineq11

Ineq13

Ineq12

Ineq15

Correct answer:

Ineq11

Explanation:

Begin by solving for :

2x > 16-6

2x > 10

x> 5

Now, this is represented by drawing an open circle at 6 and graphing upward to infinity:

Ineq11

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Example Question #1 : Negative Numbers

0>x>y>z

Quantity A: x-z

Quantity B: x+y

Possible Answers:

The relationship cannot be determined from the information given.

Quantity B is greater

Quantity A is greater

The two quantities are equal

Correct answer:

Quantity A is greater

Explanation:

Since both quantities have an , you can ignore this variable, which will give you and for quantities A and B, respectively. Since and are both negative numbers, must be bigger than , which means that no matter what numbers they are, Quantity A must be bigger.

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Example Question #1 : How To Subtract Negative Numbers

If and are integers such that $-9\leq a\leq 4$ and -2 < b < 10 , what is the smallest possible value of b-a ?

Possible Answers:

Correct answer:

Explanation:

To make b-a as small as possible, let be as small as possible (b=-1) , and subtract the largest value of possible (a=4) :

-1-4=-5

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Example Question #2 : How To Subtract Negative Numbers

Quantity A:

7-4-(-3)-8

Quantity B:

8-(-8)-1+2

Which of the following is true?

Possible Answers:

The relationship between the quantities cannot be determined.

Quantity B is larger.

Quantity A is larger.

The two quantities are equal in size.

Correct answer:

Quantity B is larger.

Explanation:

A problem like this one is very easy. All you need to do is manage your arithmetic well. Remember that when you subtract a negative number, this is the same as adding the positive of that number. Therefore, you can rewrite each of your quantities:

Quantity A:

7-4-(-3)-8=7-4+3-8

Using a calculator, this comes out to be:

Quantity B:

8-(-8)-1+2=8+8-1+2

Using a calculator, this comes out to be:

Therefore, quantity B is larger.

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Example Question #711 : Gre Quantitative Reasoning

Simplify $(7+x+3x^{4})-(x^{4}+x-2)$

Possible Answers:

$4x^{4}+2x+5$

$2x^{4}+2x+9$

$2x^{4}+5$

$2x^{4}+9$

$2x^{4}+2x+5$

Correct answer:

$2x^{4}+9$

Explanation:

The answer is $2x^{4}+9$

Make sure to distribute negatives throughout the second half of the equation.

$(7+x+3x^{4})-(x^{4}+x-2)$

$(3x^{4}+x+7)+(-x^{4}-x+2)$

$2x^{4}+9$

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Example Question #2 : Negative Numbers

Solve for :

2x + 47 = -47

Possible Answers:

x = -57

x = -37

x = 47

x = -94

x = -47

Correct answer:

x = -47

Explanation:

To solve this problem, you need to get your variable isolated on one side of the equation:

2x + 47 = -47

2x + 47 + (- 47) = -47 + (-47)

Taking this step will elminate the on the side with :

2x = -94

Now divide by to solve for :

$x = -\frac{94}{2}$

x = -47

The important step here is to be able to add the negative numbers. When you add negative numbers, they create lower negative numbers (if you prefer to think about it another way, you can think of adding negative numbers as subtracting one of the negative numbers from the other).

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Example Question #6 : Negative Numbers

Solve for :

2x + 52 = -30

Possible Answers:

x = 31

x = -31

x = 41

x = 51

x = -41

Correct answer:

x = -41

Explanation:

To solve this problem, first you must add to both sides of the problem. This will yield a result on the right side of the equation of , because a negative number added to a negative number will create a lower number (i.e. further away from zero, and still negative). Then you divide both sides by two, and you are left with x = -41 .

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Example Question #134 : Arithmetic

Find the value of .

$-2x= -\frac{1}{3}$

Possible Answers:

$\frac{1}{6}$

$-\frac{1}{6}$

Correct answer:

$\frac{1}{6}$

Explanation:

To solve for , divide each side of the equation by -2.

$\left(-\frac{1}{3}\right) \div-2$ is the same as

$-\frac{1}{3} \cdot -\frac{1}{2}$ which is POSITIVE $\frac{1}{6}$

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GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : How To Graph An Inequality With A Number Line

Example Question #124 : Arithmetic

Example Question #562 : Arithmetic

Example Question #1 : Negative Numbers

Example Question #1 : How To Subtract Negative Numbers

Example Question #2 : How To Subtract Negative Numbers

Example Question #711 : Gre Quantitative Reasoning

Example Question #2 : Negative Numbers

Example Question #6 : Negative Numbers

Example Question #134 : Arithmetic

All GRE Math Resources

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