GRE Math : Integers
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Example Questions
Example Question #141 : Integers
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?
12
14
16
10
8
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 : How To Find The Number Of Integers Between Two Other Integers
Quantity A: The number of possible values of 
Quantity B: 31
The information cannot be determined from the information given.
Quantity A is greater
The two quantities are equal
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 #142 : 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 : How To Find Absolute Value
Quantitative Comparison:
Column A
|–3 + 4|
Column B
|–3| + |4|
Column A and B are equal
Column B is greater
Cannot be determined
Column A is greater
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 : How To Find Absolute Value
Quantitative Comparison
|x – 3| = 3
Quantity A: x
Quantity B: 2
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
The relationship cannot be determined from the information given.
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 #3 : 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 #4 : How To Find Absolute Value
Quantitative Comparison
Quantity A: (|–4 + 1| + |–10|)2
Quantity B: |(–4 + 1 – 10)2|
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
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 #3 : How To Find Absolute Value
Quantity A:
Quantity B:
The relationship cannot be determined from the information given
Quantity B is greater
The two quantities are equal
Quantity A is greater
Quantity B is greater
If 
Example Question #4 : 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 #12 : Operations
Evaluate:
3 + 2(1 * 9 + 8) – 9/3
36
82
34
76/3
37/3
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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