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16 Mar 2011, 03:36
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Is p divisible by 168
1) p is divisible by 14
2) p is divisible by 12
The way i solved it is the following
Consider Statement 1 alone
prime factors of 168
2*2*2*3*7= 2^3*3*7
Since 14 is a factor of 168 and P is divisble by 14 (7*2), then keeping in mind the factor foundation rule, p should also be divisible by 168/
Statement 1 sufficient
So A/D
Consider Statement 2 alone
Since 12 is a factor of 168, (12*14), then due to factor foundation rule, p is divisble by 12 and is divisble by 168 ( factor foundation rule )
So statement 2 sufficient
So answer is D
Please tell me your way of solving this ?
Am i using the factor foundation rule correctly ?
1) p is divisible by 14
2) p is divisible by 12
The way i solved it is the following
Consider Statement 1 alone
prime factors of 168
2*2*2*3*7= 2^3*3*7
Since 14 is a factor of 168 and P is divisble by 14 (7*2), then keeping in mind the factor foundation rule, p should also be divisible by 168/
Statement 1 sufficient
So A/D
Consider Statement 2 alone
Since 12 is a factor of 168, (12*14), then due to factor foundation rule, p is divisble by 12 and is divisble by 168 ( factor foundation rule )
So statement 2 sufficient
So answer is D
Please tell me your way of solving this ?
Am i using the factor foundation rule correctly ?
vivesomnium
Joined: 09 Feb 2011
Last visit: 18 Mar 2018
Posts: 174
Own Kudos:
Given Kudos: 13
Concentration: General Management, Social Entrepreneurship
Schools: HBS '14 (A)
GMAT 1: 770 Q50 V47
16 Mar 2011, 04:17
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Factor foundation says that factor of a factor is a factor.
Therefore, if P is divisible by 168, then it would be divisible by 14 and 12.
You are using it wrongly in reverse. --> 168 is a multiple of 14 not factor.
For example, lets say that P =84. P is divisible by 12 (12X7) and 14 (14X6), but P is not divisible by 168. (84/168= 0.5, not an integer, hence not divisible.)
Answer would be both statements together are not sufficient. (E)
Hope this clarifies.
Therefore, if P is divisible by 168, then it would be divisible by 14 and 12.
You are using it wrongly in reverse. --> 168 is a multiple of 14 not factor.
For example, lets say that P =84. P is divisible by 12 (12X7) and 14 (14X6), but P is not divisible by 168. (84/168= 0.5, not an integer, hence not divisible.)
Answer would be both statements together are not sufficient. (E)
Hope this clarifies.
16 Mar 2011, 04:44
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Hi vivesomnium, Thanks for your help on this. So basically the factors, factor are also factors. Just have another quick question for you.
Is pq divisble by 168
1) p is divisble by 14
2)q is divisble by 12
In my eyes, the answer is E, because statement 1 is insufficient alone, since we dont know q, and statement 2 is insufficient since we dont knoe p. And taken together, we still dont know since 168 is not a factor of 14 and 12
Is pq divisble by 168
1) p is divisble by 14
2)q is divisble by 12
In my eyes, the answer is E, because statement 1 is insufficient alone, since we dont know q, and statement 2 is insufficient since we dont knoe p. And taken together, we still dont know since 168 is not a factor of 14 and 12
