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Problem 14 Section 11 of 100DS

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Problem 14 Section 11 of 100DS

Post Thu Jan 25, 2007 3:44 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If a and b are positive integers, is a/b=2/3?

    (1) 3a = 2b
    (2) For integers m and n, a = 2m and b = 3n

    Is not D the the answer? if you substitute 2m by a and 3n by b the result is m=n.

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    Post Wed Jan 31, 2007 5:08 pm
    yes/no: is a/b = 2/3

    (1) 3a = 2b. Can be rearranged to a/b = 2/3. Yes.

    (2) a = 2m, b = 3n, m and n are integers. So a/b = 2m/3n. We don't know what m and n are; we only know they are integers.

    Nor do we know that m = n; we can't just substitute into the equation given in the question stem b/c we don't know that that equation is true - the point is that we're being asked to determine whether it is true. m could equal n IF that equation is true (that is, if a/b = 2/3 is true). But if it isn't true, then m and n can be any integers. So can't tell for sure.

    Answer is A.

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    Cybermusings Legendary Member Default Avatar
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    Post Wed Mar 28, 2007 5:15 am
    If a and b are positive integers, is a/b=2/3?

    (1) 3a = 2b
    (2) For integers m and n, a = 2m and b = 3n

    3a = 2b

    Thus a/b = 2/3

    Hence I is sufficient

    a = 2m and b = 3n

    Thus a/ b = 2m/3n

    But here a/b will be equal to 2/3 if m = n

    Hence it may or may not be true

    Hence II is insufficient

    Thus A

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