Divisibilty

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ygdrasil24: Senior | Next Rank: 100 Posts; Posts: 42; Joined: Tue Dec 06, 2011 8:06 amFollowed by: 1 member; Thanked: 3 times

by ygdrasil24 » Sun May 26, 2013 9:53 pm

Which of the following CANNOT yield an integer when divided by 7 ?
(A) The sum of three consecutive integers
(B) An integer with only even prime factors
(C) The product of two odd integers
(D) An integer divisible by 8
(E) An even integer

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Source: Beat The GMAT — Problem Solving | Sun May 26, 2013 9:53 pm

aaggar7: Master | Next Rank: 500 Posts; Posts: 124; Joined: Sun Mar 11, 2012 8:48 pmFollowed by: 1 member; Thanked: 9 times

by aaggar7 » Mon May 27, 2013 3:23 am

IMO B.

A. 6 +7+ 8 = 21 - divisible by 7

C. 7 * 3 = 21 - divisible by 7

D. 56 - divisible by 7 and 8

E. 42 - divisible by 7

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Mon May 27, 2013 6:23 am

ygdrasil24 wrote:Which of the following CANNOT yield an integer when divided by 7 ?
(A) The sum of three consecutive integers
(B) An integer with only even prime factors
(C) The product of two odd integers
(D) An integer divisible by 8
(E) An even integer

We can also reword the question as, "Which of the following is not divisible by 7?"
In order for an integer (say N) to be divisible by 7, it must be the case that 7 is in the prime factorization of N.

Answer choice B: If the only prime factors are even, there's no way that 7 can be in the prime factorization. So, B is correct.

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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sana.noor: Legendary Member; Posts: 512; Joined: Mon Jun 18, 2012 11:31 pmFollowed by: 20 members; Thanked: 42 times

by sana.noor » Mon May 27, 2013 6:40 am

it should be B, an integer with only even prime factors

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deepsea13: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Sun Jun 12, 2011 7:47 amFollowed by: 1 member

by deepsea13 » Tue May 28, 2013 2:55 am

I solved this problem by POE.

A) Say, your three consecutive integers are 6, 7 and 8. On adding and dividing by 7, we get an integer.

B) Wasn't sure how to go about this, so skipped ahead.

C) 7 x 7 = 49. Yields and integer when we divide by 7.

D) 56/8 = 7. Divide by 7, you get an integer.

E) 14. Divide by 7, an integer.

SO, leaves me with B.

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