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# If K is a 5-digit positive integer, is K divisible by 4?

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Joined: 02 Sep 2009
Posts: 52430
If K is a 5-digit positive integer, is K divisible by 4?  [#permalink]

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12 Apr 2018, 20:36
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Difficulty:

15% (low)

Question Stats:

81% (00:41) correct 19% (00:46) wrong based on 47 sessions

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If K is a 5-digit positive integer, is K divisible by 4?

(1) The tens digit and the units digit of K are 3 and 6, respectively.
(2) K is divisible by 12.

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Re: If K is a 5-digit positive integer, is K divisible by 4?  [#permalink]

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12 Apr 2018, 21:04
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Bunuel wrote:
If K is a 5-digit positive integer, is K divisible by 4?

(1) The tens digit and the units digit of K are 3 and 6, respectively.
(2) K is divisible by 12.

CONCEPT: A number will be divisible by 4 if last two digits of number are divisible by 4 e.e. 256 is divisible by 4 because 56 is divisible by 4

Question : is K divisible by 4?

Statement 1: The tens digit and the units digit of K are 3 and 6, respectively.

SInce last two digits of the number are 36 which is divisible by 4 therefore K will be divisible by 4

SUFFICIENT

Statement 2: K is divisible by 12

12 = 4*3 i.e. for a number to be divisible by 12 the number must be divisible by 4 and 3 both.

i.e. K is divisible by 4 hence

SUFFICIENT

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Re: If K is a 5-digit positive integer, is K divisible by 4?  [#permalink]

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26 Apr 2018, 20:11
I) Divisibility rule of 4
If last 2 digit i.e. unit and tens digit is divisible by 4 for any number then that number is divisible by 4

Here 36 is divisible by 4 so K is divisible by 4
Sufficient

II)if number is divisible by 12 then number will always be divisible by it's factors in this case, 3,4,6 and 2 are factors of 12 so K is divisible by each one of them also

So sufficient

Ans D

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Re: If K is a 5-digit positive integer, is K divisible by 4? &nbs [#permalink] 26 Apr 2018, 20:11
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