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Three dice, each of which has its 6 sides numbered 1

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Three dice, each of which has its 6 sides numbered 1

by jjjinapinch » Mon Aug 07, 2017 9:10 am

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Three dice, each of which has its 6 sides numbered 1 through 6, are tossed. The sum of the 3 numbers that are facing up is 12. Is at least 1 of these numbers 5?

(1) None of the 3 numbers that are facing up is divisible by 3
(2) Of the numbers that are facing up, 2, but not all 3, are equal

Official Guide question
Answer: C
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Source: — Data Sufficiency |

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by ceilidh.erickson » Mon Aug 07, 2017 10:25 am

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First, write out the possibilities of 3 dice that sum to 12, since the possibilities are finite:

6, 5, 1
6, 4, 2
6, 3, 3
5, 5, 2
5, 4, 3
4, 4, 4

Since order doesn't matter, these are the only combinations. The ones with at least one 5 are highlighted in red.

When evaluating the statements, see if you can find an example WITHOUT 5's as well as one with 5's.

(1) None of the 3 numbers that are facing up is divisible by 3
Which of our examples fit here?
5, 5, 2 --> "yes" answer to question
4, 4, 4 --> "no" answer to question
Insufficient.

(2) Of the numbers that are facing up, 2, but not all 3, are equal
Which of our examples fit here?
6, 3, 3 --> "no" answer to question
5, 5, 2 --> "yes" answer to question
Insufficient.

(1) & (2) Together:
Which of our examples fit BOTH statements?
5, 5, 2 --> this is the only example that fits both.
This gives us a definitive "yes" answer to the question.
Sufficient.

The answer is C.

Btw, this is DS #315 in OG 2017.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
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