Is the Positive Integer n a Multiple of 24? GMAT Data Sufficiency

Question: Is the positive integer n a multiple of 24?

1. n is a multiple of 4.
2. n is a multiple of 6.

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are not sufficient.

“Is the positive integer n a multiple of 24?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "The Official GMAT Guide for Quantative Revie". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiencycomprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation

Approach Solution 1:

There is no difference between saying that 12 is a multiple of 4 and that 12 is divisible by 4.

As for the question.
Is the positive integer n a multiple of 24?

(1) n is a multiple of 4. Not sufficient.
(2) n is a multiple of 6. Not sufficient.

(1)+(2) n is a multiple of both 4 and 6 which means that it's a multiple of least common multiple of 4 and 6, which is 12. So, even taken together statements are not sufficient, since n can be for example 12 as well as 24.

Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: E

Approach Solution 2:

We need to find out if the positive integer n a multiple of 24 ?

Statement 1 says n is a multiple of 4.
Statement 2 says n is a multiple of 6.

Solution:
Is n= 24I where I is an Integer

Statement 1:
n=4a where "a" is an integer.
Now If n=4 then no but n=48 then yes.
A and D are ruled out

Statement 2:
If n=6 then no if n=24 then yes.

Combining we get n is muliple of 4 and 6
Hence, n is a mulitple of 12 but need not be a multiple of 24.
The reason is:

If n=12,36,60 then not a mutiple of 24, but
If n= 24,48 then Yes

Statements (1) and (2) TOGETHER are not sufficient.Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: E

Approach Solution 3:

To find: "n" multiple of 24
24 x _ = "n"

Statement 1:
"n" is a multiple of 4
4 x A = n
A can be any number as we don't have any specific value of "n"
NOT SUFFICIENT

Statement 2:
"n" is a multiple of 6
6 x B = n
B can be any number as we dont have any specific value of "n"
NOT SUFFICIENT

Combining...
4 x A = n
6 x B = n
"n" can be
12 -> Not a multiple of 24
24 -> yes a multiple of 24
NOT SUFFICIENT

Statements (1) and (2) TOGETHER are not sufficient.Statements (1) and (2) TOGETHER are not sufficient.

Correct Answer: E

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