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Bunuel
Is p divisible 168?

(1) p is divisible by 14
(2) p is divisible by 12

Bunuel

I have seen an answer on theManhattan Prep form by a Manhattan Prep instructor saying both are sufficient together (C), but then I see that the Manhattan Prep book says both together are insufficient (E).

What do you think?
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woohoo921
Bunuel
Is p divisible 168?

(1) p is divisible by 14
(2) p is divisible by 12

Bunuel

I have seen an answer on theManhattan Prep form by a Manhattan Prep instructor saying both are sufficient together (C), but then I see that the Manhattan Prep book says both together are insufficient (E).

What do you think?

DmitryFarber

There cannot be any controversy on this whatsoever. The answer is E.

p is divisible by 14 and p is divisible by 12 means that p is divisible by the least common multiple of 14 (14 = 2*7) and 12 (12 = 2^2*3), which is 7*2^2*3 = 84. So, if p is 84, then the answer to the question is NO but if p is say 168, then the answer is YES.
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Bunuel, I think he means some other problem where p is divisible by m*n .. so instead of taking the LCM you multiply the primes (so that extra prime that derives only from multiplication is sufficient to answer - whereas here - you need an extra prime)
Bunuel
woohoo921
Bunuel
Is p divisible 168?

(1) p is divisible by 14
(2) p is divisible by 12

Bunuel

I have seen an answer on theManhattan Prep form by a Manhattan Prep instructor saying both are sufficient together (C), but then I see that the Manhattan Prep book says both together are insufficient (E).

What do you think?

DmitryFarber

There cannot be any controversy on this whatsoever. The answer is E.

p is divisible by 14 and p is divisible by 12 means that p is divisible by the least common multiple of 14 (14 = 2*7) and 12 (12 = 2^2*3), which is 7*2^2*3 = 84. So, if p is 84, then the answer to the question is NO but if p is say 168, then the answer is YES.
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