divisibility question!

[chaitanya.bhansali]

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.

[[email protected]]

Hi chaitanya.bhansali,

If you don't want to use strategic approaches on the GMAT, then you're likely going to run into pacing problems and a limit to how high you can score. That having been said, you can approach this DS question mathematically, using prime factorization.

The question asks "Is X divisible by 12?"; this essentially asks..."when you prime factor X, do you have AT LEAST a 3 and two 2s?" This is a YES/NO question.

Fact 1: X is divisible by 27.

By prime factoring 27, we find that X contains AT LEAST three 3s (3x3x3 = 27), but we don't know anything else about X.

IF X also contains two (or more) 2s, then the answer to the question is YES.
IF X does NOT contain two (or more) 2s, then the answer to the question is NO.
Fact 1 is INSUFFICIENT

Fact 2: X is divisible by 6.

By prime factoring 6, we find that S contains AT LEAST one 2 and one 3 (2x3 = 6), but we don't know anything else about X.

IF X contains another 2, then the answer to the question is YES.
IF X does NOT contain another 2, then the answer to the question is NO.
Fact 2 is INSUFFICIENT

Combined, we know that X contains one 2 and three 3s (not four 3s...the 3 from Fact 2 is already "counted" in Fact 1), but we don't know anything else about X.

IF X contains another 2, then the answer to the question is YES.
IF X does NOT contain another 2, then the answer to the question is NO.
Combined, INSUFFICIENT.

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

[GMATinsight]

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

[Brent@GMATPrepNow]

Is x divisible by 12?

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

A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N

Consider these examples:
24 is divisible by 3 because 24 = (2)(2)(2)(3)
Likewise, 70 is divisible by 5 because 70 = (2)(5)(7)
And 112 is divisible by 8 because 112 = (2)(2)(2)(2)(7)
And 630 is divisible by 15 because 630 = (2)(3)(3)(5)(7)

Now onto the question.....

Target question: Is x divisible by 12?
Since 12 = (2)(2)(3), we can REPHRASE the target question as....

REPHRASED target question: Are there two 2's and one 3 hiding within the prime factorization of x?

Statement 1: x is divisible by 27
27 = (3)(3)(3), so we know that there are three 3's hiding within the prime factorization of x. So, we have the one 3 taken care of but can we be also certain that there are two 2's hiding within the prime factorization of x? NO
So, statement 1 is NOT SUFFICIENT

Statement 1: x is divisible by 6
6 = (2)(3), so we know that there is one 2 and one 3 hiding within the prime factorization of x. So, we have the one 3 taken care of but can we be also certain that there are two 2's hiding within the prime factorization of x? NO
So, statement 2 is NOT SUFFICIENT


Statements 1 and 2 combined
Statement 1 tells us that there are three 3's hiding within the prime factorization of x
Statement 2 tells us that there is one 2 and one 3 hiding within the prime factorization of x
Combined, we can be certain that there are three 3's AND one 2 hiding within the prime factorization of x.
So, we still have NOT guaranteed that there is one 3 AND two 2's hiding within the prime factorization of x.
Since we cannot be certain that answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

[chaitanya.bhansali]

Thanks everyone for your prompt replies, really appreciate it!

[Brent@GMATPrepNow]

Here are a few more questions that require us to understand the relationship between divisibility and prime factorization:
https://www.beatthegmat.com/factors-t272765.html
https://www.beatthegmat.com/do-t-and-12- ... 74544.html
https://www.beatthegmat.com/is-xy-a-mult ... 74522.html
https://www.beatthegmat.com/confused-nee ... 71655.html
https://www.beatthegmat.com/multiple-of-990-t272719.html
https://www.beatthegmat.com/if-n-t-3-for ... 48420.html

Cheers,
Brent

[Matt@VeritasPrep]

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.