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Number divisibility

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Source: — Data Sufficiency |
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by GMATGuruNY » Thu Apr 02, 2015 9:48 am
prachi18oct wrote:Is n/18 an integer?

a) 5n/18 is an integer.
b) 3n/18 is an integer.
Statement 1: 5n/18 is an integer
If 5n/18 = 1, then n=18/5.
In this case, n/18 is not an integer.
If 5n/18 = 5, then n=18.
In this case, n/18 is an integer.
INSUFFICIENT.

Statement 2: 3n/18 is an integer
If 3n/18 = 1, then n=18/3=6.
In this case, n/18 is not an integer.
If 3n/18 = 3, then n=18.
In this case, n/18 is an integer.
INSUFFICIENT.

Statements combined:
5n/18 - 3n/18 = 2n/18.
Since both 5n/18 and 3n/18 are integers, we get:
2n/18 = 5n/18 - 3n/18 = integer - integer = integer.

3n/18 - 2n/18 = n/18.
Since both 3n/18 and 2n/18 are integers, we get:
n/18 = 3n/18 - 2n/18 = integer - integer = integer.
SUFFICIENT.

The correct answer is C.
Last edited by GMATGuruNY on Thu Apr 02, 2015 10:50 am, edited 1 time in total.
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by [email protected] » Thu Apr 02, 2015 9:54 am
Hi prachi18oct,

This question is ultimately about 'factoring' and understanding what it really means for a fraction to equal an integer.

We're asked if N/18 is an integer. This is a YES/NO question.

Fact 1: 5N/18 is an integer

For this fraction to be an integer, 18 must divide evenly into 5N.

So...5N could = 18, 36, 54, 72, 90, etc.....
Thus, N is a multiple of 3.6

IF....
5N = 18
N = 3.6
3.6/18 is NOT an integer and the answer to the question is NO

IF....
5N = 90
N = 18
18/18 IS an integer and the answer to the question is YES
Fact 1 is INSUFFICIENT

Fact 2: 3N/18 is an integer

For this fraction to be an integer, 18 must divide evenly into 3N.

So...3N could = 6, 12, 18, 24.....90, etc.
Thus, N is a multiple of 6

IF...
N = 6
6/18 is NOT an integer and the answer to the question is NO

IF....
N = 18
18/18 IS an integer and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know....
N is a multiple of 3.6
N is a multiple of 6

N COULD be 0, 18, 36, 54, etc.

All of these possibilities ARE multiples of 18, so N/18 will ALWAYS be an integer and the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

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by Brent@GMATPrepNow » Thu Apr 02, 2015 10:01 am
One small point: Many students answer this question incorrectly, because they assume that n is an INTEGER.
If n were, indeed, an integer, then the correct answer would be A.
However, since we can't assume that n is an integer, the correct answer is C (for the reasons stated in the above posts).

Cheers,
Brent
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