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Is b/3 an integer?

This topic has 1 expert reply and 0 member replies

Is b/3 an integer?

Post Tue Sep 12, 2017 10:30 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Is b/3 an integer?

    (1) (b^2-9)/3 is an integer.
    (2) p and p + 1 are prime factors of b.

    OA is B.

    Statement 2 confuses me. Can any expert help me.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Tue Sep 12, 2017 12:29 pm
    Vincen wrote:
    Is b/3 an integer?

    (1) (b² - 9)/3 is an integer.
    (2) p and p + 1 are prime factors of b.
    Target question: Is b/3 an integer?

    Statement 1: (b² - 9)/3 is an integer
    There are several values of b that satisfy statement 1. Here are two:
    Case a: b = 6. Here, (b² - 9)/3 = (6² - 9)/3 = (36 - 9)/3 = 27/3 = 9, and 9 is an integer. In this case, b/3 = 6/3 = 2. So, b/3 IS an integer
    Case b: b = √18. Here, (b² - 9)/3 = (√18² - 9)/3 = (18 - 9)/3 = 9/3 = 3, and 3 is an integer. In this case, b/3 = (√18)/3 = (3√2)/3 = √2 (. So, b/3 is NOT an integer
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: p and p + 1 are prime factors of b
    Notice that p and p+1 are CONSECUTIVE integers
    Since p and p+1 are CONSECUTIVE integers, we know that one of the numbers must be odd and one must be even.
    Since 2 is the ONLY even integer, we can conclude that p = 2 and p+1 = 3
    Since p and p+1 are factors of b, we can see that b is divisible by 2 and by 3.
    If b is divisible by 3, then b/3 must be an integer
    Since we can answer the target question with certainty, statement 2 is SUFFICIENT

    Answer: B

    Cheers,
    Brent

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