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Is 12 a factor of the positive integer n?

This topic has 1 expert reply and 0 member replies

Is 12 a factor of the positive integer n?

Post Thu Nov 09, 2017 4:10 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is 12 a factor of the positive integer n?

    (1) n is a factor of 36.
    (2) 3 is a factor of n.

    What's the best way to determine which statement is sufficient?

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    Post Thu Nov 09, 2017 4:32 pm
    ardz24 wrote:
    Is 12 a factor of the positive integer n?

    (1) n is a factor of 36.
    (2) 3 is a factor of n.
    Target question: Is 12 a factor of the positive integer n?

    Statement 1: n is a factor of 36
    This statement doesn't FEEL sufficient, so I'll TEST some values.
    There are several values of n that satisfy statement 1. Here are two:
    Case a: n = 12, in which case 12 IS a factor of n
    Case b: n = 6, in which case 12 is NOT a factor of n
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: 3 is a factor of n
    Once again, there are several values of n that satisfy statement 2. Here are two:
    Case a: n = 12, in which case 12 IS a factor of n
    Case b: n = 6, in which case 12 is NOT a factor of n
    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
    In other words,
    Case a: n = 12, in which case 12 IS a factor of n
    Case b: n = 6, in which case 12 is NOT a factor of n
    Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

    Answer: E

    Cheers,
    Brent

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    Thanked by: ardz24
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