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If a represents a single digit and the four digit integer a12a is

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If a represents a single digit and the four digit integer a12a is  [#permalink]

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New post 22 Oct 2017, 20:17
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A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

84% (00:35) correct 16% (00:46) wrong based on 44 sessions

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If a represents a single digit and the four digit integer a12a is divisible by 6, what is a?

(a) 2
(b) 3
(c) 4
(d) 6
(e) 7

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Re: If a represents a single digit and the four digit integer a12a is  [#permalink]

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New post 22 Oct 2017, 21:05
D. 6

You want a12a to be a multiple of 6. Thus, sum 1+2+2a should be divisible by 3 and ‘a’ should be even. So, only possible value that satisfies the above constraints is 6.


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Re: If a represents a single digit and the four digit integer a12a is  [#permalink]

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New post 23 Oct 2017, 07:23
To be divisible by 2 the units digit should be either 0,2,4,6,8. So a or c or d. And to be divisible by 3 sum of digits should be divisible by 3. Only option d satisfies the conditions.

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Re: If a represents a single digit and the four digit integer a12a is  [#permalink]

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New post 23 Oct 2017, 07:36
6

1) For the number to be divisible by 6, it has to be divisible by 2 & 3.
2) Since the number is divisible by 2, it must be even.
3) Since the number must be divisible by 3, the sum of digits of the number must be divisible by 3.

We can now arrive at the answer by simply eliminating the answer choices.

For pt.3 to hold good, options b and d will satisfy.
Among these, for pt.2 to hold good, only option d satisfies.


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Re: If a represents a single digit and the four digit integer a12a is &nbs [#permalink] 23 Oct 2017, 07:36
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