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# M12-27

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Math Expert
Joined: 02 Sep 2009
Posts: 43361

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15 Sep 2014, 23:47
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Question Stats:

82% (00:50) correct 18% (01:13) wrong based on 92 sessions

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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
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43361

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15 Sep 2014, 23:47
2
KUDOS
Expert's post
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 $$x = 4$$. $$4104 = 36*114$$.

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Joined: 19 May 2016
Posts: 29
Location: United States
Concentration: Strategy, Human Resources
GMAT 1: 710 Q46 V41
GMAT 2: 730 Q49 V41
GMAT 3: 680 Q46 V37
WE: Operations (Manufacturing)

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02 Sep 2016, 05:47
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 $$x = 4$$. $$4104 = 36*114$$.

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.
Intern
Joined: 30 Jun 2016
Posts: 7

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13 Sep 2016, 23:55
2
KUDOS
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 $$x = 4$$. $$4104 = 36*114$$.

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.
Intern
Joined: 29 Sep 2016
Posts: 16
Location: United States
Concentration: Finance, Economics
GPA: 3.01

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09 Nov 2016, 14:57
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
Manager
Joined: 02 Feb 2016
Posts: 89
GMAT 1: 690 Q43 V41

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27 Apr 2017, 11:54
Can someone explain why does it have to be divisible by 3 if its divisible by 36?
Math Expert
Joined: 02 Sep 2009
Posts: 43361

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28 Apr 2017, 01:56
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Expert's post
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.
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Manager
Joined: 02 Feb 2016
Posts: 89
GMAT 1: 690 Q43 V41

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28 Apr 2017, 02:15
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..!
Director
Joined: 02 Sep 2016
Posts: 784

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23 Aug 2017, 04:14
x10x is divisible by 36 (2^2*3^2) when x is even and x+1+0+x is divisible by 3.

4 is even and 4+1+0+4= 9 which is divisible by 3.
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Re: M12-27   [#permalink] 23 Aug 2017, 04:14
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# M12-27

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