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On a certain sight seeing tour. . .

This topic has 1 expert reply and 0 member replies

On a certain sight seeing tour. . .

Post Fri Sep 22, 2017 10:16 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    On a certain sight seeing tour, the ration of the number of women to number of children was 5 to 2, What was the number of men on the sigh seeing tour

    (1) On the sight seeing tour, the ratio of number of children to the number of men was 5 to 11
    (2) The number of women on the sight seeing tour was less than 30

    The OA is C.

    This question is very difficult to me. Can any expert explain me how to solve it?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Fri Sep 22, 2017 2:09 pm
    Quote:
    On a certain sightseeing tour, the ratio of the number of women to the number of
    children was 5 to 2. What was the number of men on the sightseeing tour?

    (1) On the sightseeing tour, the ratio of the number of children to the number of men was 5 to 11.
    (2) The number of women on the sight-seeing tour was less than 30.

    Let W = # of women
    Let M = # of men
    Let C = # of children

    Target question: What is the value of M?

    Given: The ratio of the number of women to the number of children was 5 to 2
    In other words, W : C = 5 : 2

    Statement 1: On the sight-seeing tour, the ratio of the number of children to the number of men was 5 to 11.
    In other words, C : M = 5 : 11

    Let's combine this ratio with the given ratio (W : C = 5 : 2)
    To do so, we'll find some EQUIVALENT RATIOS such that they both share a term.

    Take 5 : 2 and multiply both terms by 5 to get 25 : 10
    So, W : C = 25 : 10

    Now take 5 : 11 and multiply both terms by 2 to get 10 : 22
    So, C : M = 10 : 22

    At this point, we can combine the ratios to get W : C : M = 25 : 10 : 22
    As you can see this just tells us the ratios of the variables, it does not provide enough information to find the exact value of M
    Consider these three conflicting possibilities:
    Case a: W : C : M = 25 : 10 : 22
    Case b: W : C : M = 50 : 20 : 44
    Case c: W : C : M = 75 : 30 : 66
    etc.
    Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: The number of women on the sight-seeing tour was less than 30.
    There's no information at all about the men so statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Statement 1 essentially tells us that W : C : M = 25 : 10 : 22, so with each ratio that's equivalent to 25 : 10 : 22, we can a different value of M
    So, we could have W : C : M = 25 : 10 : 22
    or W : C : M = 50 : 20 : 44
    or W : C : M = 75 : 30 : 66
    etc.
    Statement 2 reduces the possible number of women (W).
    If W < 30, then there's only ONE possible ratio that works. That is W : C : M = 25 : 10 : 22
    This means that there MUST be 22 men
    Since we can answer the target question with certainty, the combined statements are SUFFICIENT

    Answer = C

    Cheers,
    Brent

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