I am having a hard time understanding a point in MGMAT's

Question

I am having a hard time understanding a point in MGMAT's number properties book. It asks the question: Is P divisible 168? (1) p is divisible by 14 (2) p is divisible by 12 It then goes on to state that p is divisible by 7, 2......and 3, 2^2. I get this point, so I initially assumed that 168 was divisible by 7, 3, and 2^3. It seems that the answer in my mind would be that both statements together make the statement true, however MGMAT states that it is indeterminable becuase 2 of the 2's overlap. It states that combined, 14 and 12 have primes 7, 3, and 2^2. It don't get this...can someone please explain this to me.

atish · Answer

Pretty simple actually,

since you already know that 14 is div by 2,7
and 12 is div by 2,2,3

Now if P is divisible by both 14 & 12 then it has to be div by 2,2,3,7 so P could be 84 (LCD). But still not divisible 168 (I guess now that common multiple 2 makes sense).

Hope this help!

CaliCpa · Answer

I definitely see your point. Maybe I am just overthinking this. For these types of problems, is it easiest to just take the LCM, and if it is less than what the question is asking for (i.e. 168), then you know its a "maybe" or "indeterminable?" I feel pretty comfortable with the LCM and GCF calculations.

jolt · Answer

I wouldn't recommend this method. It is much better to try to understand what the question is actually asking and break it down.

This is asking whether P is divisible by 2^3, 7, and 3

(1) Says P is divisible by 2 and 7 (insufficient, we don't know if it is divisible by the remaining factors of 168)
(2) Says P is divisible by 2^2 and 3 (insufficient, we are still missing a 2 and 7)

Together says P is divisible by 2^2, 3, and 7 (because it is possible that the 2 from statement 1 and one of the 2s from statement 2 are in fact the same 2) so it is still insufficient

For example, if Statement two said P was divisible by 24, (which is divisible by 2^3 and 3) then we could say P is divisible by 168.

It will also help you to know that "factors, prime numbers, and divisibility" all mean the same thing

bb · Answer

Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/
Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/

No posting of PS/DS questions is allowed in the main Math forum.

Bunuel · Answer

Yes quite so. But consider this, in some cases we would be able to say that number (p in your case) is not divisible by some number.

Let's consider your case:

Is p divisible by 168?

(1) p is divisible by 14=2*7 Not sufficient
(2) p is divisible by 12=2^2*3 Not sufficient

(1)+(2) LCM 84--> p is for sure divisible by 84, but for 168 we don't know. Still not sufficient.

Let's consider another case say:

Is p divisible by 168?

(1) p is divisible by 84
(2) p is not divisible by any integer n>1 in power of 3

The answer would be different.

bumpbot · Answer

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I am having a hard time understanding a point in MGMAT's

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