GRE Math : Arithmetic
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Example Questions
Example Question #142 : Integers
Quantitative Comparison
|x – 3| = 3
Quantity A: x
Quantity B: 2
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Quantity A is greater.
The relationship cannot be determined from the information given.
It's important to remember that absolute value functions yield two equations, not just one. Here we have x – 3 = 3 AND x – 3 = –3.
Therefore x = 6 or x = 0, so the answer cannot be determined.
If we had just used the quation x – 3 = 3 and forgotten about the second equation, we would have had x = 6 as the only solution, giving us the wrong answer.
Example Question #2 : How To Find Absolute Value
Quantitative Comparison
Quantity A: |10| – |16|
Quantity B: |1 – 5| – |3 – 6|
Quantity B is greater.
Quantity A is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Quantity A: |10| = 10, |16| = 16, so |10| – |16| = 10 – 16 = –6.
Quantity B: |1 – 5| = 4, |3 – 6| = 3, so |1 – 5| - |3 – 6| = 4 – 3 = 1.
1 is bigger than –6, so Quantity B is greater.
Example Question #2 : How To Find Absolute Value
Quantitative Comparison
Quantity A: (|–4 + 1| + |–10|)2
Quantity B: |(–4 + 1 – 10)2|
Quantity B is greater.
The relationship cannot be determined from the information given.
Quantity A is greater.
The two quantities are equal.
The two quantities are equal.
Quantity A: |–4 + 1| = |–3| = 3 and |–10| = 10, so (|–4 + 1| + |–10|)2 = (3 + 10)2 = 132 = 169
Quantity B: |(–4 + 1 – 10)2| = |(–13)2| = 169
The two quantities are equal.
Example Question #1 : How To Find Absolute Value
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
Quantity B is greater
If 
Example Question #143 : Integers
What is the absolute value of the following equation when 
(–3)3 = –27. Any time a negative number is cubed, it remains negative. –27 + 5 = –22. The absolute value of any number will ALWAYS be positive so the absolute value of –22 is 22. This is our answer.
Example Question #1 : How To Find Order Of Operations
Evaluate:
3 + 2(1 * 9 + 8) – 9/3
82
34
37/3
76/3
36
34
Order of operations
Do everything inside the parenthesis first:
3 + 2(17) – 9/3
next, do multiplication/division
3 + 34 – 3
= 34
Example Question #216 : Arithmetic
3 + 4 * 5 / 10 – 2 =
7
1.5
3
5.5
5
3
Here we must use order of operations. First we multiply 4 * 5 = 20. Then 20 / 10 = 2. Now we can do the addition and substraction. 3 + 2 – 2 = 3. If you started at the beginning on the left hand side and not used order of operations, you would mistakenly choose 1.5 as the correct answer.
Example Question #151 : Integers
Order of operations can be remembered by PEMDAS (Please Excuse My Dear Aunt Sally): Parentheses Exponents Multiplication Division Addition Subtraction.
[7(5 + 2) – (5 * 8)]2 =
1: Inner parentheses = [ 7(7) – 40 ]2
2: Outer brackets = [ 49 – 40 ]2 = 92
3: Exponents = 81
Example Question #152 : Integers
This looks daunting as one long equation, but let's look at each piece and then add them all together.
2–3 = 1/23 = 1/8
250 = 1
(–218)1 = –218
6251/4 = 5
(–27)1/3 = –3
Then, 2–3 + 250 + (–218)1 + 7/8 – 6251/4 + (–27)1/3 = 1/8 + 1 – 218 + 7/8 – 5 – 3 = –224.
Example Question #1 : Percentage
What percentage of a solution is blood if it contains 
First, you must find the total amount of solution. This is 
Now, the percentage of the solution that is blood can be represented:
This is the same as 
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