# GRE Math : How to evaluate algebraic expressions

## 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 ?

Explanation:

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

Working backwards,

### Example Question #12 : Evaluating Expressions

Quantity A                 Quantity B

35

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

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

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### Example Question #13 : Evaluating Expressions

In a four-digit positive interger , the thousand's digit is three times the units digit.

Quantitiy A                Quantitiy B

Unit's digit of                  4

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

Quantity B is greater.

Explanation:

If we set the quantities equal, and the units digit of  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 . Therefore Quantity B is greater.

### Example Question #11 : Evaluating Expressions

The arithmetic mean of is 6. What is the value of ?

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.

If we subtract  from , you are left with  so therefore  must sum to .

### Example Question #11 : Evaluating Expressions

If and , what is the value of ?

Explanation:

If you add all three equations together you get

### 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?

4

7

5

2

6

7

Explanation:

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 so 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 thus we know we have two$1 bills

this is the number of \$5 bills

### Example Question #11 : How To Evaluate Algebraic Expressions

Given these equations, what is the value of ?

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 , what is one possible value for ?

Explanation:

When you plug in  into , you get , which equals 900.

### Example Question #19 : Evaluating Expressions

Quantity A:

Quantity B:

The two quantities are equal

Quantity A is greater

Quantity B is greater

The relationship cannot be determined from the information given

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?