GRE Math : Integers
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Example Questions
Example Question #201 : Arithmetic
Miles is 3 years older than Ashley. Ashley is 5 years younger than Bill. How old is Ashley if together the three of their ages sum to 44?
16
14
8
10
12
12
Miles is 3 years older than Ashley, so M = A + 3. Also, Bill is 5 years older than Ashley, so B = A + 5. Together the three of their ages sum to 44, thus:
A + A + 3 + A + 5 = 44
3A + 8 = 44
3A = 36
A = 12
Example Question #1 : Counting
Quantity A: The number of possible values of 
Quantity B: 31
The information cannot be determined from the information given.
The two quantities are equal
Quantity A is greater
Quantity B is greater
Quantity B is greater
An integer with a units digit of 5 occurs once every 10 consecutive integers. There are 300 integers between 200 and 500, so there must be 30 values with a units digit of 5.
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
In a certain game, integers are called magic numbers if they are multiples of either 
How many magic numbers are there in the game between 
There are 13 "magic" numbers: 3,4,6,8,9,12, their negative counterparts, and 0.
Example Question #1 : Absolute Value
Quantitative Comparison:
Column A
|–3 + 4|
Column B
|–3| + |4|
Column A is greater
Column B is greater
Cannot be determined
Column A and B are equal
Column B is greater
The operations in the absolute value are always done first. So in Column A, |–3 + 4| = |1| = 1. In Column B, |–3| + |4| = 3 + 4 = 7.
Example Question #2 : Absolute Value
Quantitative Comparison
|x – 3| = 3
Quantity A: x
Quantity B: 2
The two quantities are equal.
Quantity B is greater.
The relationship cannot be determined from the information given.
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 #1 : How To Find Absolute Value
Quantitative Comparison
Quantity A: |10| – |16|
Quantity B: |1 – 5| – |3 – 6|
The relationship cannot be determined from the information given.
Quantity A is greater.
The two quantities are equal.
Quantity B is greater.
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 A is greater.
The relationship cannot be determined from the information given.
Quantity B 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 #214 : Arithmetic
Quantity A:
Quantity B:
Quantity A is greater
The two quantities are equal
The relationship cannot be determined from the information given
Quantity B is greater
Quantity B is greater
If 
Example Question #6 : How To Find Absolute Value
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 #211 : Arithmetic
Evaluate:
3 + 2(1 * 9 + 8) – 9/3
36
37/3
82
76/3
34
34
Order of operations
Do everything inside the parenthesis first:
3 + 2(17) – 9/3
next, do multiplication/division
3 + 34 – 3
= 34
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