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Divisibilty

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Divisibilty

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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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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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.

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Brent
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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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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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