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If each of the three nonzero numbers a, b, and c is divisibl

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Carcass

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Joined: 18 Apr 2015

Posts: 16976

GRE 1: Q160 V160

If each of the three nonzero numbers a, b, and c is divisibl [#permalink]

21 Apr 2018, 04:58

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11% (00:57) wrong

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If each of the three nonzero numbers a, b, and c is divisible by 3, then abc must be divisible by which one of the following the numbers?

(A) 8
(B) 27
(C) 81
(D) 121
(E) 159

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amorphous

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Joined: 07 Jan 2018

Posts: 730

Re: If each of the three nonzero numbers a, b, and c is divisibl [#permalink]

25 Apr 2018, 01:53

$A,B, and C$ are non zero integer divisible by $3$so at minimum $a=3,b=3,c=3$
therefore abc at minimum $= 27$ and abc should be a multiple of $27$
option B
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ScottTargetTestPrep

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Joined: 12 Sep 2018

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Re: If each of the three nonzero numbers a, b, and c is divisibl [#permalink]

07 Apr 2019, 17:45

Expert Reply

Carcass wrote:

If each of the three nonzero numbers a, b, and c is divisible by 3, then abc must be divisible by which one of the following the numbers?

(A) 8
(B) 27
(C) 81
(D) 121
(E) 159

We see that a = 3r, b = 3s and c = 3t for some nonzero integers r, s, and t. Therefore, abc = (3r)(3s)(3t) = 27rst. We see that abc must be divisible by 27.

Answer: B
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