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Divisible by 27?

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by Amrabdelnaby » Tue Dec 15, 2015 11:11 am
Dear Pros,
I figured statement one and two but can't figure out statement three: whether the number is divisible by 27 or not.

Please help.

Thanks

If n is a 27-digit positive integer, all of whose digits are the same, which of the following must be true?

i:: n is divisible by 3

ii:: n is divisible by 9

iii: n is divisible by 27

A) i only
B) i and ii only
C) i and iii only
D) ii and iii only
E) i, ii, and iii
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by GMATGuruNY » Tue Dec 15, 2015 11:50 am
Amrabdelnaby wrote:Dear Pros,
I figured statement one and two but can't figure out statement three: whether the number is divisible by 27 or not.
An integer whose digits sum to a multiple of 9 is ITSELF a multiple of 9.

111 = 3*37.

Thus:
111,111,111,111,111,111,111,111,111

= 3 * (037,037,037,037,037,037,037,037,037)

= 3 * (integer whose digits sum to 90)

= 3 * (multiple of 9)

= multiple of 27.
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