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A number 15B is divisible by 6

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A number 15B is divisible by 6 [#permalink] New post 14 Nov 2012, 07:37
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A
B
C
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E

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A number 15B is divisible by 6. Which of thse will be true about the positive integer B?

(A) B will be even
(B) B will be Odd
(C) B will be divisible by 6
(D) Both a & b
(E) A, B and C
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Re: A number 15B is divisible by 6 [#permalink] New post 14 Nov 2012, 07:59
vomhorizon wrote:
A number 15B is divisible by 6. Which of thse will be true about the positive integer B?

(A) B will be even
(B) B will be Odd
(C) B will be divisible by 6
(D) Both a & b
(E) A, B and C


15B is divisible by 6
=> 3*5*B is divisible by 3*2
=> 5*B is divisible by 2
=> B has to be even.

Ans A it is.
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Re: A number 15B is divisible by 6 [#permalink] New post 15 Feb 2013, 03:44
vomhorizon wrote:
A number 15B is divisible by 6. Which of thse will be true about the positive integer B?

(A) B will be even
(B) B will be Odd
(C) B will be divisible by 6
(D) Both a & b
(E) A, B and C



15B/6 = integer

Since we know that prime numbers of 15 are 3 and 5, B has to have at least one 2 so that the result can be an integer.
Moreover, B has to be even since it has at least one 2.
Correct answer is A.
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Re: A number 15B is divisible by 6 [#permalink] New post 15 Feb 2013, 06:28
Expert's post
I'd solve this the same way as Vips did above, but if you notice that B can be equal to 2 here, then you can also see immediately that the answer is A.
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Re: A number 15B is divisible by 6   [#permalink] 15 Feb 2013, 06:28
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A number 15B is divisible by 6

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