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Positive integer n divisible by 4 and 21 [#permalink]
 19 Jul 2009, 10:00
Question Stats:
0% (00:00) correct
 0% (00:00) wrong based on 0 sessions
This question and answer explanation is from a Manhattan GMAT practice test. I don't understand why they don't take into account the 7 as one of the prime factors. Can anyone explain this? Thanks for your help. If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following? 8 - 2, 2, 2 12 - 2, 2, 3 18, 2, 3, 3 24 - 2, 2, 2, 3 48- , 2, 2, 2, 2, If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3. The correct answer is B.
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Joined: 19 Jun 2009
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Concentration: Strategy, General Management
GMAT 1: 650 Q51 V27
GMAT 2: 710 Q48 V39
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Re: Positive integer n divisible by 4 and 21 [#permalink]
19 Jul 2009, 11:08
You are confused. Read the question again, carefully. If you still don't get it, here it is - Now, prime factors : 4= 2, 2. 21=3,7. 'n' is divisible by 4 & 21. Consider, Y is divisor after dividing 'n' by 4 & 21. Let's write 'n' as n = 4 x 21 x Y = 2 x 2 x 3 x 7 x Y. Now, question asks for a number that divides 'n'. If there is a number that divides 'n' for sure, it must not have any additional prime factors than (2,2,3,7). Consider the possibility that Y might even be 1, so we don't consider Y here. All other options except '12'=2 x 2 x 3, have those additional prime factors. This is complete logic. Quick way to solve the problem - Divide 4 x 21 by each option given. The one which gives integer divisor, is your answer. 
_________________
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Re: Positive integer n divisible by 4 and 21 [#permalink]
22 Jul 2009, 00:16
well explained alpeshvc.
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Re: Positive integer n divisible by 4 and 21 [#permalink]
23 Jul 2009, 04:31
In Other way, the first number,apart from 0, is LCM of 4 and 21. This is 84. so out of the following only 12 divides it. Thanks. nss123 wrote: This question and answer explanation is from a Manhattan GMAT practice test. I don't understand why they don't take into account the 7 as one of the prime factors. Can anyone explain this? Thanks for your help. If positive integer n is divisible by both 4 and 21, then n must be divisible by which of the following? 8 - 2, 2, 2 12 - 2, 2, 3 18, 2, 3, 3 24 - 2, 2, 2, 3 48- , 2, 2, 2, 2, If n is divisible by both 4 and 21, its prime factors include 2, 2, 3, and 7. Therefore, any integer that can be constructed as the product of these prime factors is also a factor of n. In this case, 12 is the only integer that can definitively be constructed from the prime factors of n, since 12 = 2 x 2 x 3. The correct answer is B. |
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Re: Positive integer n divisible by 4 and 21
[#permalink]
23 Jul 2009, 04:31
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