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

This topic has 1 expert reply and 0 member replies
jjjinapinch Senior | Next Rank: 100 Posts Default Avatar
Joined
24 Jul 2017
Posted:
83 messages

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

Post Mon Aug 07, 2017 9:10 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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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    Post Mon Aug 07, 2017 10:25 am
    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.

    _________________


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    EdM in Mind, Brain, and Education
    Harvard Graduate School of Education


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