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M12-27

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M12-27 [#permalink]

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New post 16 Sep 2014, 00:47
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Official Solution:

If \(x10x\) is a four-digit integer, what is digit \(x\), if \(x10x\) is divisible by 36?

A. 2
B. 3
C. 4
D. 6
E. 7

To be divisible by 36, \(x10x\) has to be even and a multiple of 3. This leaves us with \(x = 4\). \(4104 = 36*114\).

Answer: C
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Re: M12-27 [#permalink]

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New post 02 Sep 2016, 06:47
Bunuel wrote:
Official Solution:

If \(x10x\) is a four-digit integer, what is digit \(x\), if \(x10x\) is divisible by 36?

A. 2
B. 3
C. 4
D. 6
E. 7

To be divisible by 36, \(x10x\) has to be even and a multiple of 3. This leaves us with \(x = 4\). \(4104 = 36*114\).

Answer: C


Great explanation. I used the same apprach, but instead of dividing, I just added the digits (from 1 to 9) to see if the sum is divisible by 3. Obviously, some can be easily discarded like 1 and 5.

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Re: M12-27 [#permalink]

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New post 14 Sep 2016, 00:55
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Bunuel wrote:
Official Solution:

If \(x10x\) is a four-digit integer, what is digit \(x\), if \(x10x\) is divisible by 36?

A. 2
B. 3
C. 4
D. 6
E. 7

To be divisible by 36, \(x10x\) has to be even and a multiple of 3. This leaves us with \(x = 4\). \(4104 = 36*114\).

Answer: C


x10x is divisible by 36, meaning that x10x is divisible by 4 also. The sign of divisible by 4 is that 0x is divisible by 4. So x will be only 4 or 8. Look up all choices, only 4 appears.

We don't need to do any calculation but still find the correct answer.

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Re: M12-27 [#permalink]

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New post 09 Nov 2016, 15:57
Perhaps, easier number to work with is 9 because 36 is divisible by 9 by looking at the sum of the numbers (3+6)

Thus the sum of digits in the answer choices must be divisible by 9.

Don't even have to write down anything, but doing simple addition in mind conclude us with C. 4+1+0+4 = 9

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Re: M12-27 [#permalink]

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New post 27 Apr 2017, 12:54
Can someone explain why does it have to be divisible by 3 if its divisible by 36?

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Re: M12-27 [#permalink]

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New post 28 Apr 2017, 02:56
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Re: M12-27 [#permalink]

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New post 28 Apr 2017, 03:15
Bunuel wrote:
TheMastermind wrote:
Can someone explain why does it have to be divisible by 3 if its divisible by 36?


Because 36 = 3*12. If integer x is divisible by integer y, then x is divisible by all factors of y too.


Thank you so much, Bunuel..!

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Re: M12-27 [#permalink]

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New post 23 Aug 2017, 05:14
x10x is divisible by 36 (2^2*3^2) when x is even and x+1+0+x is divisible by 3.

4 is the answer.
4 is even and 4+1+0+4= 9 which is divisible by 3.
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Re: M12-27   [#permalink] 23 Aug 2017, 05:14
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