Divisibility

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relaxin99: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Sep 16, 2008 4:33 pm; Thanked: 2 times

by relaxin99 » Wed Feb 04, 2009 8:16 pm

Is the interger K divisible by 4?

1) 8k is divisible by 16
2) 9k is divisible by 12

With the answer, can you all please explain how you came up with the answer thanks

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 04, 2009 8:16 pm

DanaJ: Site Admin; Posts: 2567; Joined: Thu Jan 01, 2009 10:05 amFollowed by: 550 members; Thanked: 712 times; GMAT Score:770

by DanaJ » Thu Feb 05, 2009 12:36 am

1. is insufficient, since if 8k is divisible by 16, this means that 8k = 16d (where d = quotient when you divide 8k by 16). This means that k = 2d, which means that k is even. However, we cannot tell if it is divisible by 4. If d is odd, then it sure isn't.

2. is sufficient, since if 9k is divisible by 12, this means that 9k = 12d (again, d = quotient). Since 9 is not divisible by 4 but it is divisible by 3, this means that k must be divisible by 12/3 = 4.
So k is divisible by 4.

Answer B.

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relaxin99: Senior | Next Rank: 100 Posts; Posts: 73; Joined: Tue Sep 16, 2008 4:33 pm; Thanked: 2 times

by relaxin99 » Fri Feb 06, 2009 4:46 pm

THank you very much Dana....wonderful explanation here

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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

by cramya » Sat Feb 07, 2009 1:18 am

Stmt I

k=2 NO
k=4 YES

insuff

Stmt II

9k/12 = a (where a is some integer)

3k/4 = a

3 is not divisible by 4 so k must be divisible by 4 for 3k/4 to be an INTEGER

SUFF

Choose A

Regards,
CR

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