GRE Math : Arithmetic

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #2 : How To Find Value With A Number Line

If perimeter of equilateral triangle is , what is the height of the triangle?

Possible Answers:

Correct answer:

Explanation:

Since perimeter of equilateral triangle is  and we have three equal sides, we just divide that vaue by  to get . To find height, we can set-up a proportion. 

The height is opposite the angle . Side opposite  is  and the side of equilateral triangle which is opposite  is .

 Cross multiply.

 Divide both sides by 

 

Let's simplify by factoring out  to get a final answer of 

Example Question #692 : Arithmetic

On a real number line, x1 = -4 and x2 = 14. What is the distance between these two points?

Possible Answers:

-18

4

18

10

Correct answer:

18

Explanation:

The distance between two points is always positive. We calculate lx2 - x1l, which will give us the distance between the points.

|14- (-4)| = |14+4| = |18| = 18

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

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

Possible Answers:

Ineq24

Ineq25

Ineq22

Ineq21

Ineq23

Correct answer:

Ineq21

Explanation:

To begin, you must simplify so that you "isolate" , (i.e. at least eliminate any coefficients from it). To do this, divide all of the members of the inequality by :

Now, this inequality represents all of the numbers between 13 and 32.  However, it does include  (hence, getting a closed circle for that value) and does not include  (hence, getting an open circle for that value). Therefore, it looks like:

Ineq21

Example Question #561 : Arithmetic

Ineq3

Which of the following inequalities is represented by the number line shown above?

Possible Answers:

Correct answer:

Explanation:

Since the inequality represents one range of values between two end points (both of which are included, given the sign being "less than or equal"), you know that whatever you answer, it must be convertible to the form:

Now, you know that it is impossible to get this out of the choices that have no absolute values involved in them. Therefore, the only options that make sense are the two having absolute values; however, here you should choose only the ones that have a , for only that will yield a range like this. Thus, we can try both of our options.

The wrong answer is simplified in this manner:

And you can stop right here, for you know you will never have  for the left terminus.

The other option is simplified in this manner:

This is just what you need!

Example Question #5 : Number Line

Quantity A: 

Quantity B: 

Possible Answers:

Quantity B is larger.

The two quantities are equal.

The relationship cannot be determined.

Quantity A is larger.

Correct answer:

Quantity B is larger.

Explanation:

It is not necessary to solve this problem by multiplying terms out. Notice that between quantities A and B, the last three terms switch places for the two large numbers. as such they can be rewritten:

Quantity A:

Quantity B:

 

Both quantities A and B share the exact same terms, save for two:

Quantity A: 

Quantity B: 

From visual inspection, it is clear that B is larger.

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

Numberline1

Which of the following is true?

Possible Answers:

Correct answer:

Explanation:

Since  is always positive, and , it follows that  for all possible values.

For the A, it is possible to choose values that make the statement false, for example  and .

C is always false.

Example Question #124 : Arithmetic

Numberline2

Which of the statements is always true?

Possible Answers:

Correct answer:

Explanation:

Although C may approach zero for large values of  and values of , 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 

For B,  would make the value zero.

Example Question #2 : How To Graph An Inequality With A Number Line

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

Possible Answers:

Ineq14

Ineq15

Ineq11

Ineq13

Ineq12

Correct answer:

Ineq11

Explanation:

Begin by solving for :

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

Ineq11

Example Question #121 : Arithmetic

Quantity A:

Quantity B:

Possible Answers:

The relationship cannot be determined from the information given.

The two quantities are equal

Quantity A is greater

Quantity B is greater

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.

Example Question #122 : Arithmetic

If  and  are integers such that   and , what is the smallest possible value of ?

Possible Answers:

 

Correct answer:

 

Explanation:

To make  as small as possible, let  be as small as possible , and subtract the largest value of  possible :

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