D.S -Number System

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Tue Sep 13, 2011 5:17 am

Hi,
Please post a detailed solution to the below one. I often gets confused..

Is the positive integer p a multiple of the positive integer q
1- p/3q is an integer
2- 3p/7q is an integer

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Source: Beat The GMAT — Data Sufficiency | Tue Sep 13, 2011 5:17 am

cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Tue Sep 13, 2011 5:41 am

p is multiple of q means p=nq where n is an integer. or p/q = n
a) p/3q is an integer -> p/q = integer*3 = n (where n is an integer)
True
b) 3p/7q is an integer. or p/q = 7*integer/3. Now it is possible that integer is not multiple of 3, and thus p/q is not an integer. It is also possible that integer is multiple of 3, and p/q is an integer. thus insufficient.
IMO A

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sl750: Master | Next Rank: 500 Posts; Posts: 496; Joined: Tue Jun 07, 2011 5:34 amFollowed by: 1 member; Thanked: 38 times

by sl750 » Tue Sep 13, 2011 6:17 am

The prompt asks, is p=q*i, where i is some integer

In statement 1, we have p/3q = integer. This means that p should at least have a factor of both 3 and q in order to be divisible by 3q. Therefore, p/q=3*integer. If you substitute this back in to the main equation, is p=q*i, we get, Is 3*integer=i ?. Sufficient

In statement 2, we have 3p/7q = integer. Using the same reasoning, p should at least have a factor of 7 and q in order to be divisible by 7q. Therefore, p=7/3*integer. Substituting this back in to the main equation, we get, Is 7/3*integer =i ? If the integer is a multiple of 3, the result will be an integer, whereas, if it is a non-multiple of 3, the result will be a fraction. Insufficient

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imhimanshu: Senior | Next Rank: 100 Posts; Posts: 87; Joined: Sat Feb 28, 2009 7:01 am; Location: India; Thanked: 2 times

by imhimanshu » Tue Sep 13, 2011 6:48 am

Thanks for the reasoning. It helped me !

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