divisible by 2, 3, and 15

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sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Thu Nov 17, 2011 3:16 am

If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45

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Source: Beat The GMAT — Problem Solving | Thu Nov 17, 2011 3:16 am

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Thu Nov 17, 2011 3:20 am

sanju09 wrote:If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45

k is divisible by 2, 3, and 15, so for k + x to be divisible by these numbers x should also be divisible by all these numbers.From the options, only 20 and 30 are divisible by 2, and only 30 is divisible by 3(between 20 and 30), so Option D - k+30

Last edited by neelgandham on Thu Nov 17, 2011 3:22 am, edited 1 time in total.

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kmittal82: Master | Next Rank: 500 Posts; Posts: 324; Joined: Mon Jul 05, 2010 6:44 amFollowed by: 3 members; Location: London; Thanked: 70 times

by kmittal82 » Thu Nov 17, 2011 3:20 am

I'm sure there's an "algebraic" way of doing this, but its much simpler to test it with k = 30 (which is the lowest k divisible by 2,3 and 15)

Plugging k = 30, (D) is the only option which is still divisible by 2,3 and 15

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Abhishek009: Master | Next Rank: 500 Posts; Posts: 359; Joined: Wed Mar 11, 2009 4:37 amFollowed by: 2 members; Location: Kolkata, India; Thanked: 50 times

by Abhishek009 » Thu Nov 17, 2011 6:52 am

sanju09 wrote:If k is divisible by 2, 3, and 15, which of the following is also divisible by these numbers?
(A) k + 5
(B) k + 15
(C) k + 20
(D) k + 30
(E) k + 45

2 , 3 and 15 are co prime numbers...

Now to find the least common no which is divisible by 2, 3 and 15 we take the LCM of the numbers which is 30....

Hence k = 30

Again we need to find the number , divisible by the no's will be by checking the options individually -

A. 30 +5 which is not divisible by 2 and 3

B. 30+15 which is not divisible by 2 and 3

C. 30+20 which is not divisible by 2 and 3

D. 30 + 30 which is divisible by 2 and 3 and 15...

Hence answer will be D..

Abhishek

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