chaitanya.bhansali wrote:i don't want to solve this question (or similar questions) by picking numbers, how would i solve this?

Is x divisible by 12?

1) x is divisible by 27.
2) x is divisible by 6.

Thanks.

Question : Is x divisible by 12?
The answer has to be in YES or NO

but for x to be divisible by 12, it should be divisible by 3 as well as 4 [Because 12 = 3 x 4]

Rephrased Question : Is x Divisible by 3 as well as 4?

Statement 1)x is divisible by 27
This only communicates that x is divisible by 3 [3 being the factor of 27]
but we are clueless whether x is divisible by 4 or not therefore No concrete answer to the question in form of YES or NO
INSUFFICIENT

Statement 2)x is divisible by 6
This only communicates that x is divisible by 3 as well as by 2 [6 = 2x3, 2 and 3 being the factor of 27]
but we are clueless whether x is divisible by 4 or not [because 4 requires 2 power of 2 but here we have just one power of 2 for sure] therefore No concrete answer to the question in form of YES or NO
INSUFFICIENT

Combining the two statements

We understand that x is divisible 3 and 2 but we can not be sure whether x is divisible by 4 therefore Insufficient

Answer: Option E

Thanks everyone for your prompt replies, really appreciate it!

chaitanya.bhansali wrote:i don't want to solve this question (or similar questions) by picking numbers, how would i solve this?

Is x divisible by 12?

1) x is divisible by 27.
2) x is divisible by 6.

Thanks.

I think you're right to avoid picking numbers on divisibility questions: these questions are so common that you need to understand them, and once you understand them you can answer them much more quickly if get the concepts.

For instance, if x is divisible by 12, we can interpret that statement in one of two ways, whichever you prefer:

1:: x is a multiple of 12
2:: x has a 3 and two 2s in its prime factorization (since 12 = 3 * 2 * 2).

So our question is really "Is x a multiple of 12?" or "Does x has a 3 and two 2s in its prime factorization?"

S1 tells us that x is a multiple of 27. Some multiples of 27 (such as 27*4) are also multiples of 12; some others (such as 27*2) are NOT multiples of 12. So S1 is INSUFFICIENT. The conceptual key here is that S1 tells us that x divides by 3 (because 27 divides by 3), but NOT whether x divides by 4. Since 12 = 3*4, we can't answer the question.

S2 tells us that x is a multiple of 6. Some multiples of 6 (such as 6*2) are multiples of 12; some aren't, such as 6*3. Conceptually, this tells us that x divides by 6, or by 3*2, but not that x divides by 3*2*2, or 12.

S1+S2 together tells us that x is a multiple of 27 and a multiple of 6. Some multiples of 6 and 27, such as 6*27, are NOT divisible by 12; some others, such as 6*27*2, ARE divisible by 12. STILL insufficient! Conceptually, we know this will be insufficient because we still don't have to have 2*2 in any of our multiples, and to divide by 12 we need to divide by 2*2.