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3 integers: x, y, z if there is a multiple of 7?

This topic has 1 expert reply and 0 member replies

Top Member

3 integers: x, y, z if there is a multiple of 7?

Post Thu Nov 09, 2017 1:26 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    3 integers: x, y, z if there is a multiple of 7?
    1: x + y + z is a multiple of 7
    2: xyz is a multiple of 7

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    GMAT/MBA Expert

    Post Thu Nov 09, 2017 7:02 pm
    Let's rephrase the prompt as

    Quote:
    x, y, and z are all integers. Is at least one of them a multiple of 7?
    S1::

    x + y + z = 7 * some integer

    We could have 1 + 2 + 4, or we could have 7 + 14 + 21; NOT SUFFICIENT.

    S2::

    xyz = 7 * some integer

    Since each side consists entirely of integers, each side must have the same prime factorization. Since 7 appears in the prime factorization of the right side, it must also appear in the prime factorization of the left side. That means that at least one of x, y, and z contains a factor of 7 in its prime factorization, so one of them must divide by 7.

    Thanked by: mihai9
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