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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # If each of the three nonzero numbers a, b, and c is divisible by 3, th

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Math Expert V
Joined: 02 Sep 2009
Posts: 59725
If each of the three nonzero numbers a, b, and c is divisible by 3, th  [#permalink]

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Difficulty:   15% (low)

Question Stats: 92% (00:45) correct 8% (00:59) wrong based on 38 sessions

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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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Joined: 13 Jan 2018
Posts: 341
Location: India
Concentration: Operations, General Management
GMAT 1: 580 Q47 V23 GMAT 2: 640 Q49 V27 GPA: 4
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Re: If each of the three nonzero numbers a, b, and c is divisible by 3, th  [#permalink]

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1
As a,b and c each are divisible by 3, every number contains atleast one 3.

Let a = 3x, b = 3y, c = 3z

Product a*b*c = 27*xyz.

This product must always be divisible by 27 regardless of x,y, and z.

OPTION: B
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3158
If each of the three nonzero numbers a, b, and c is divisible by 3, th  [#permalink]

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Solution

Given:
• a, b, and c non-zero numbers divisible by 3.

To find:
• abc must be divisible by which of given number.

Approach and Working:
Each a, b, and c are divisible by 3. Hence, we can assume:
• a = 3p, where p is a non-zero number.
• Similarly, b = 3q and c = 3r where q and r are non-zero numbers.

Therefore, abc = 3p * 3q * 3r = 27 * p * q * r.
Hence, abc is definitely divisible by 27.

Thus, the correct answer is option B.

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GMAT Club Legend  V
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Re: If each of the three nonzero numbers a, b, and c is divisible by 3, th  [#permalink]

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Bunuel 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

given a,b,c are all multiples of 3
so least value of a,b,c ; 27 ; considering them all to be 3
so 27 hsa to least no a,b,c must be divisible by
IMO b
Target Test Prep Representative V
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Re: If each of the three nonzero numbers a, b, and c is divisible by 3, th  [#permalink]

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Bunuel 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.

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If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: If each of the three nonzero numbers a, b, and c is divisible by 3, th   [#permalink] 07 Apr 2019, 18:45
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# If each of the three nonzero numbers a, b, and c is divisible by 3, th  