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What is the probability that a three-digit integer corresponding with the three numbers thrown on three different d

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by Max@Math Revolution » Mon Jan 27, 2020 6:20 pm
[GMAT math practice question]

What is the probability that a three-digit integer corresponding with the three numbers thrown on three different dice is a multiple of 11?

A. 1/3
B. 2/27
C. 4/27
D. 5/27
E. 2/9
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Re: What is the probability that a three-digit integer corresponding with the three numbers thrown on three different d

by Max@Math Revolution » Mon Jan 27, 2020 6:20 pm
=>

In order for a three-digit integer abc to be a multiple of 11, a – b + c must be a multiple of 11 since we have 100a + 10b + c = 99a + a + 11b – b + c = (99a + 11b) + a – b + c = 11(9a+b) + a – b +c.

If a – b + c = 0, then the possible cases for (a, b, c) are
(1, 2, 1), (1, 3, 2), (1, 4, 3), (1, 5, 4), (1, 6, 5), (2, 3, 1), (2, 4, 2), (2, 5, 3), (2, 6, 4), (3, 4, 1), (3, 5, 2), (3, 6, 3), (4, 5, 1), (4, 6, 2) and (5, 6, 1), and we have 15 cases.

If a – b + c = 11, then we have only the case (a, b, c) = (6, 1, 6).

Thus the probability is 16/(6^3) = 16/216 = 2/27.

Therefore, the answer is B.
Answer: B
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