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# Is a three-digit integer x divisible by 6?

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Joined: 02 Sep 2009
Posts: 49496
Is a three-digit integer x divisible by 6?  [#permalink]

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06 Oct 2017, 05:06
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Difficulty:

35% (medium)

Question Stats:

79% (01:13) correct 21% (01:07) wrong based on 57 sessions

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Is a three-digit integer x divisible by 6?

(1) The sum of the tens and hundreds digits of x is 6
(2) The units digit of x is 6

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Joined: 05 Jul 2006
Posts: 1731
Re: Is a three-digit integer x divisible by 6?  [#permalink]

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06 Oct 2017, 08:24
Bunuel wrote:
Is a three-digit integer x divisible by 6?

(1) The sum of the tens and hundreds digits of x is 6
(2) The units digit of x is 6

for a number to be divisible by 6 , sum of its digits has to be divisible by 3 and the number is even

let the number be in the form abc

from 1

a+b = 6 ... no mention to c ... insuff

from 2

c = 6 number is even but no mention to what a,b are... insufficient

both

in abc , a+b+c = 12 ( divisible by 3 ) and c is even = 6 .... thus number is divisible by 6 .... C
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Re: Is a three-digit integer x divisible by 6?  [#permalink]

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06 Oct 2017, 16:35
Bunuel wrote:
Is a three-digit integer x divisible by 6?

(1) The sum of the tens and hundreds digits of x is 6
(2) The units digit of x is 6

The answer should be C as follows.

For a number to be divisible by 6 it must be divisible by both 2 and 3.

Let the number be mnp

(1) The sum of the tens and hundreds digits of x is 6
As per the given condition m+n=6, but there is no mention of the property of p. p could be any number, however, for it to be divisible by 2 it must be even, which is not mentioned anywhere.
INSUFFICIENT

(2) The units digit of x is 6[/quote]
As per this condition p = 6, this means the number x is divisible by 2. Now we have to find out if the number is divisible by 3. In order to check this we need the sum of the digits m+n+p = m+n+6. But we do not know the value of m+n
INSIFFICIENT

Combining both the condition we get m+n+p = (m+n)+p = 6+6=12.
This is divisible by both 3. Also divisibility by 2 has already been proved while assessing condition (2)
SUFFICIENT

Hence answer is C
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Re: Is a three-digit integer x divisible by 6?  [#permalink]

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07 Oct 2017, 22:40
A number is divisible by 6 if the number is divisible by both 2 and 3

1) sum of the tens and hundredth digit is 6. hence, insufficient
2) unit digit is 6, clearly insufficient

taking both together we get sum of all the digit is equal to 12 hence it is divisible by 3 and since the number will be even it will be divisible by 2

hence x is divisible by 6

Answer C
Re: Is a three-digit integer x divisible by 6? &nbs [#permalink] 07 Oct 2017, 22:40
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# Is a three-digit integer x divisible by 6?

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