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# Positive integer n divisible by 4 and 21

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Joined: 08 Jul 2009
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Positive integer n divisible by 4 and 21 [#permalink]  19 Jul 2009, 09:00
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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.

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Manager
Joined: 19 Jun 2009
Posts: 141
Location: India
Concentration: Strategy, General Management
GMAT 1: 650 Q51 V27
GMAT 2: 710 Q48 V39
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WE: Engineering (Computer Hardware)
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Kudos [?]: 17 [0], given: 21

Re: Positive integer n divisible by 4 and 21 [#permalink]  19 Jul 2009, 10:08
You are confused.

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]  21 Jul 2009, 23:16
well explained alpeshvc.
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Re: Positive integer n divisible by 4 and 21 [#permalink]  23 Jul 2009, 03:31
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.

Re: Positive integer n divisible by 4 and 21   [#permalink] 23 Jul 2009, 03:31
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