GRE Math : How to find the number of integers between two other integers
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Example Questions
Example Question #1 : How To Find The Number Of Integers Between Two Other Integers
x = the total number of positive, odd 2 digit numbers less than 100
Column A
x
Column B
45
The quantity in column B is greater
The quantity in column A is greater
The relationship cannot be determined from the given information
The two quantities are equal
The two quantities are equal
There are 50 positive, odd numbers less than 100, and 45 of them are 2 digit numbers.
Example Question #1 : Counting
0 < x < y < z < 10
x, y, and z are integers.
Quantity A: –7
Quantity B: x + y – z
The two quantities are equal.
Quantity A is greater.
The relationship cannot be determined from the information given.
Quantity B is greater.
Quantity B is greater.
Since:
- There are only 9 integers between 0 and 10
- x, y, and z must all be unique
- They must be specifically ordered such that x < y < z
There are actually not too many ways in which these numbers can be chosen. So what we can do is find a range of answers for Quantity B, and see if 6 falls a) below b) above or c) in between the range.
For the maximum:
Note that the term (x + y) is maximized when x and y are maximum. The (–z) term is maximized when z is minimized. However, there are 2 terms in (x + y) and one term in (–z); thus intuitively it seems we should prioritize (x+y). To make x and y maximum:
0 < 7 < 8 < 9 < 10 since x, y, and z must be unique.
Thus maximum: (x + y – z) = 7 + 8 – 9 = 6
For the minimum:
Note that (x + y) is minimum when (x) and (y) are minimum, and (–z) is minimum when (z) itself is maximimized. However since there are 2 terms in (x+y) and1 of (–z) , again intuititively you should prioritize (x+y) over (-z). Then in order to make this the least number possible, x and y would be:
min(x + y – z) = 1 + 2 – 9 = –6
Thus, the range of possible answers is:
(x + y – z): [–6, 6]
and –7 is always less than this amount.
Example Question #1 : Counting
Quantity A: The number of positive even integers less than 1000
Quantity B: The number of positive odd integers less than 1000
Quantity A is greater.
The relationship cannot be determined from the information given.
The two quantities are equal.
Quantity B is greater.
Quantity B is greater.
The question asks for the number of positive even and odd integers less than 1000. Because 1000 is not included, the numbers to consider are 1 through 999. Every positive odd integer will have a corresponding even integer (1 and 2, 3 and 4, 5 and 6, etc.) until you get to 999. This gives the positive odd integers one more number than the number of positive even integers.
Example Question #1 : How To Find The Number Of Integers Between Two Other 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?
8
10
14
16
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 : 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 #141 : 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.
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