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How many integers n are there such that r < n < s?

This topic has 1 expert reply and 0 member replies

How many integers n are there such that r < n < s?

Post Sun Sep 24, 2017 7:03 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    How many integers n are there such that r < n < s?

    (1) s - r = 5
    (2) r and s are not integers.

    The OA is C.

    I tried to make this DS question. I concluded (E). The number of integers between r and s is constant and independent of r and s? I need a clarification. Please.

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Sun Sep 24, 2017 7:12 am
    Vincen wrote:
    How many integers n are there such that r < n < s?

    (1) s - r = 5
    (2) r and s are not integers.
    Target question: How many integers n are there such that r < n < s?

    Statement 1: s - r = 5
    There are two cases we need to consider.
    Case a: s and r are integers.
    For example, s=6 and r=1, in which case there are 4 integers between r and s (2, 3, 4 and 5)
    Case b: s and r are not integers.
    For example, s=6.1 and r=1.1, in which case there are 5 integers between r and s (2, 3, 4, 5, and 6)

    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: r and s are not integers
    This is definitely not enough information here to answer the target question.
    Consider these 2 cases.
    Case a: r=1.1 and s=2.1, in which case there is 1 integer between r and s (2)
    Case b: r=1.1 and s=3.1, in which case there are 2 integers between r and s (2 and 3)

    Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined:
    From statement 1, we know that there are either 4 or 5 integers between r and s, depending on whether or not r and s are integers.
    Statement 2 rules out the possibility that r and s are integers.
    If r and s are non integers, then there must be 5 integers between r and s

    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer = C

    Cheers,
    Brent

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