GRE Math : How to evaluate algebraic expressions

Study concepts, example questions & explanations for GRE Math

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Example Questions

Example Question #11 : Evaluating Expressions

Let  be a positive integer such that one less than three-eighths of  is the third prime integer. What is the value of ?

Possible Answers:

Correct answer:

Explanation:

The third prime integer is 5, since 1 is not considered a prime number.

Working backwards,

Example Question #12 : Evaluating Expressions

\dpi{100} \small -3x-5y=10

\dpi{100} \small 4x+6y=25

Quantity A                 Quantity B


    35                           \dpi{100} \small 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:

The two quantities are equal. 

Explanation:

You don't actually need to solve for the values of x and y. You just want to know the sum of x and y. Adding the two equations together you get 

\dpi{100} \small -3x-5y=10

\dpi{100} \small +4x+6y=25

_________________

\dpi{100} \small x+y=35

Example Question #13 : Evaluating Expressions

In a four-digit positive interger \dpi{100} \small y, the thousand's digit is three times the units digit.

Quantitiy A                Quantitiy B

Unit's digit of \dpi{100} \small y                 4

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 B is greater. 

Explanation:

If we set the quantities equal, and the units digit of \dpi{100} \small y is 4, then the thousands digit which is three times the units digit would be 12, which doesnt make sense at all because a digit must be one of the integers 0 through 9. So 4 is too big to be the units digit of \dpi{100} \small y. Therefore Quantity B is greater. 

Example Question #11 : Evaluating Expressions

The arithmetic mean of \dpi{100} \small 5,\ x,\ x+2,\ 7,\ and \ 8 is 6. What is the value of \dpi{100} \small x?

Possible Answers:

\dpi{100} \small 5

\dpi{100} \small 3

\dpi{100} \small 6

\dpi{100} \small 1

\dpi{100} \small 4

Correct answer:

\dpi{100} \small 4

Explanation:

The arithmetic mean is the sum of all numbers in a series divided by the number of items in the series. There are 5 items in the series, so they must sum to\dpi{100} \small 6\times 5 = 30.

If we subtract \dpi{100} \small 5+7+8 from \dpi{100} \small 30, you are left with \dpi{100} \small 10 so therefore \dpi{100} \small x+2+x must sum to \dpi{100} \small 10.

\dpi{100} \small x+2+x=10

\dpi{100} \small 2x +2=10

\dpi{100} \small 2x=8

\dpi{100} \small x=4

Example Question #11 : Evaluating Expressions

If \dpi{100} \small a+b=5\dpi{100} \small b+c=10 and \dpi{100} \small a+c=8, what is the value of \dpi{100} \small a+b+c?

Possible Answers:

\dpi{100} \small 5

\dpi{100} \small 7.5

\dpi{100} \small 10

\dpi{100} \small 23

\dpi{100} \small 11.5

Correct answer:

\dpi{100} \small 11.5

Explanation:

If you add all three equations together you get \dpi{100} \small a+b+b+c+a+c=5+10+8

\dpi{100} \small 2a+2b+2c=23

\dpi{100} \small a+b+c=\frac{23}{2}=11.5

Example Question #16 : Evaluating Expressions

Apoorwa has $117 in $1, $5, and $20 bills. She has twice as many $20's as $1's and the number of $20's times the number of $1's is one more than then number of $5's. How many $5's does Apoorwa have?

Possible Answers:

4

7

5

2

6

Correct answer:

7

Explanation:

The answer is 7.

First we know we have three variables so we need three different equations. Let x represent $1 bills, y represent $5 bills, and z represent $20 bills. Looking at the word problem we know that our equations are:

1)  1x + 5y + 20z = 117

2)  2x = z

3)  xz – 1 = y

Plug equation 2 into equation 3 to get y = x(2x) – 1. Now plug this new equation 3 and equation 2 into equation 1 giving us

1x+5(2x^{2}-1)+20(2x) =117

10x^{2}+41x-122=0

(10x+61)(x-2)=0

so (10x+61)=0

x=-6.1  but we know this isn't the answer becuase we can't have negative dollar bills and we also can't have 0.1 parts of a dollar bill. 

and (x-2)=0

x=2  thus we know we have two $1 bills

z=4

y=7 this is the number of $5 bills

Example Question #11 : How To Evaluate Algebraic Expressions

Given these equations, what is the value of ?

Possible Answers:

Correct answer:

Explanation:

If you divide the second equation by 2, you can cancel out the  terms, which would allow you to solve for , which is 3. Plugging in  into either equation will allow you to find , which is 8.

Therefore, .

Example Question #11 : Evaluating Expressions

If (x-5)^{2}=900, what is one possible value for ?

Possible Answers:

Correct answer:

Explanation:

When you plug in  into (x-5)^{2}=900, you get (-30)^{2}, which equals 900.

Example Question #19 : Evaluating Expressions

Quantity A:

Quantity B: 

Possible Answers:

The two quantities are equal

Quantity A is greater

Quantity B is greater

The relationship cannot be determined from the information given

Correct answer:

The relationship cannot be determined from the information given

Explanation:

We only know that  is greater than 0 (positive). If  is 2, then quantity A is greater. If  is less than 1, then quantity B is greater. Since we don't know if  is greater or less than 1, we can't definititvely conclude which quantity is larger.

Example Question #11 : How To Evaluate Algebraic Expressions

Arthur has 10 more dollars than Joan. If Arthur gives three of his dollars to Joan, he will have twice as many dollars as Joan. How many dollars does Arthur currently have?

Possible Answers:

Correct answer:

Explanation:

Set this up as two equations:  and . Substituting the first equation into the second, you get . Solving for this equation gives you . Since Arthur has 10 more dollars than Joan, he currently has 11 dollars.

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