confused

[grandh01]

25. If n is an integer, is
n/15 an integer?
(1)3n/15 is an integer.
(2)8n/15 is an integer.

How should go about solving this question? Personally I thought both statements are fine.
Thanks in advance.

[eagleeye]

25. If n is an integer, is
n/15 an integer?
(1)3n/15 is an integer.
(2)8n/15 is an integer.

How should go about solving this question? Personally I thought both statements are fine.
Thanks in advance.

Let's consider the statements:

(1)3n/15 is an integer.
If 3n/15 is an integer => (3/15)n =n/5 is an integer.
So, we know that n is definitely a multiple of 5 but not necessarily of 15. Insufficient.


(2)8n/15 is an integer.

(8/15)*n is an integer. Because 8 and 15 have no prime factors in common, n has to be a multiple of 15 (since n is an integer). Hence n/15 is an integer itself. Sufficient.

B is correct.

[alex.gellatly]

25. If n is an integer, is
n/15 an integer?
(1)3n/15 is an integer.
(2)8n/15 is an integer.

How should go about solving this question? Personally I thought both statements are fine.
Thanks in advance.

When you deal with questions like this you need to think of PRIME numbers.
In the statement stem it asks if n/15 is an integer. For n/15 to be an integer, then it needs to divide by 15 evenly. That means n must have both a 3 and a 5 (because 3*5 is the prime factorization of 15).

So lets look at the statements

Statement 1: 3n/15 is an integer.
That means that n must be 5 (or a multiple of 5) because 3n divides evenly by 15. For this to happen 3*n must have both a 5 and a 3. We know it has a 3, so n must be 5 (or a multiple of 5). This is insufficient because 5/15 IS NOT AN INTEGER.

Statement 2: 8n/15 is an integer
This means that n must be 15 (or a multiple of 15) because 8n divides evenly by 15. If we find the prime factorization of 8n, we get 2*2*2*n this MUST divide evenly by 3*5. The only way this can happen is if n's prime factorization has a 3*5 inside. This is sufficient because when n=3*5, it can divide by 15.

Choose B
I hope this helps.
Please ask if you have any questions

[Anurag@Gurome]

25. If n is an integer, is
n/15 an integer?
(1)3n/15 is an integer.
(2)8n/15 is an integer.

How should go about solving this question? Personally I thought both statements are fine.
Thanks in advance.

(1) 3n/15 is an integer.
If n = 5, then 3n/15 = (3 * 5)/15 = 1, which is an integer. Here n/15 = 5/15 = 1/3, not an integer.
If n = 15, then 3n/15 = 3, which is an integer. Here n/15 = 15/15 = 1, which is an integer.
No unique answer; NOT sufficient.

(2) 8n/15 is an integer.
Here, n has to be a multiple of 15. So, n/15 will be an integer; SUFFICIENT.

The correct answer is B.