If q is a multiple of n, and n is a positive integer, is 360/q an

Statement 1:-
It is given n<7
or n can be 1,2,3,4,5 and 6. This statement doesn't provide any information about q.
q can be a multiple of any number from 1 to 6.
So 360/q may or may not be an integer.
INSUFFICIENT

Statement 2:-
It is given that q<16.
q can be any number from 1 to 15.
so, 360/q may or may not be an integer.
For example: 360/q will be an integer if q is 6, but it will not be an integer if q is 13.
INSUFFICIENT

Combining statements 1 and 2
q can be a multiple of numbers 1,2,3,4,5 and 6 less than 16
let us take n= 1 and 12 and 11 as it's multiples.
360/q will be and integer if q= 12
360/q will not be an integer if q=11
INSUFFICIENT

Answer:- E

Solution:
q is a multiple of a positive integer n. So q = kn.Is 360/q interger ?

Statement1: n<7. Lets say n=2 and k=6.Then q=12 and 360/12 is integer. So yes.But.What if k=7?? q=14 and 360/14 is not an integer. So a yes and a no. Not consistent. So its not sufficient.

Statement2: q<16. Lets say q=15. Then yes, 360/q is an integer but if q = 14, then 360/q is not an integer. So a yes and a no. Not consistent and not sufficient.

Combined : Using same examples of statement1. Not sufficient.
Therefore, answer is E

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.

If q is a multiple of n, and n is a positive integer, is 360/q an integer?

(1) n < 7

(2) q < 16

In the original condition there are 2 variables (n,q) and in order to match the number of variables and equations, we need 2 more equations. Since there is 1 each in 1) and 2), C is likely the answer. Using 1) & 2) together, n=1, q=11 the answer is no, but if n=5, q=15 then the answer is yes. Thus it is not sufficient. Therefore the answer is E.

What is wrong with my thinking?

I think that A is sufficient, here is why:

n is a positive integer and smaller than 7. We are also told that q is a multiple of n. 360 would be divisibly by all positive numbers of n<7, hence if I multiply a factor with another number should that not result in a factor as well?

Thats why A seems sufficient to me, however something must be wrong...

q is a multiple of n not a factor.
consider n=3, then q can take infinite values such as 9,12,300,9000,etc. So,360/q may or may not be an integer.
If it was given that q<7, then what you are doing would have been correct.

In addition to that, If N = 1, Q can be any positive integer. But some divide 360 (1,2,3,4,5,6,8...) and some dont (7,11...).

Hence the Ans is E.

KAPLAN OFFICIAL SOLUTION:

Here we are asked to determine if 360 is evenly divisible by some number q. Make sure to note that, as n is a positive integer and q is a multiple of n, q must be a positive integer.

Statement 1 tells us that n must be less than 7. If n is 2, q can be any positive even number. Thus, q can be 12, in which case the answer to the question is ‘yes,’ OR q can be 14, in which case the answer to the question is ‘no.’ Sometimes yes, and sometimes no is insufficient in yes/no questions, therefore, statement 1 is not sufficient.

Statement 2 tells us that q must be less than 16. Just as was the case in statement 1, q can be 12, providing an answer of ‘yes,’ or q can be 14, providing an answer of ‘no.’ Again we have sometimes yes, sometimes no, which is NOT sufficient.

Looking at the statements together, we can immediately see that q could STILL equal 12 or 14 when both statements are true. Thus, together the statements are still not sufficient for the same reasons as they were insufficient alone, and your final answer choice is E or choice 5—there is not enough information here to answer the question.

E. Both statements are not enough because Q could be 14 (multiple of 2) and 360/q will not be an integer. But it is when q is 10.

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