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Results of a survey of 100 voters - Nice Question

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theCodeToGMAT Legendary Member
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Results of a survey of 100 voters - Nice Question

Post Tue Oct 08, 2013 11:58 pm
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    The table above shows the results of a survey of 100 voters each responded “favorable” or “unfavorable” or “not sure” when asked about their impressions of candidate M and of candidate N.
    What was the number of voters who responded “favorable” for both candidates?

    (1) The number of voters who did not respond “favorable” for either candidate was 40.

    (2) The number of voters who responded “unfavorable” for both candidates was 10
    {A}
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    Post Wed Oct 09, 2013 3:59 am
    Quote:
    Favorable Unfavorable Not sure
    Candidate M 40 20 40
    Candidate N 30 35 35

    The table above shows the results of a survey of 100 voters each responded favorable or unfavorable or not sure when asked about their impressions of candidate M and of candidate N. What was the number of voters who responded favorable for both candidates?

    (1) The number of voters who did not respond favorable for either candidate was 40.

    (2) The number of voters who responded unfavorable for both candidates was 10.
    Total Favorable = Favorable for M + Favorable for N - Favorable for Both

    The big idea with overlapping group problems is to SUBTRACT THE OVERLAP.
    When we count the number who responded Favorable for M and the number who responded Favorable for N, the number who responded Favorable for BOTH -- the OVERLAP -- gets counted twice.
    So that we don't double-count the overlap, it must be SUBTRACTED from the total.
    Since Favorable for M = 40 and Favorable for N = 30, we get:

    Total = 40 + 30 - both
    Both = 70 - total.

    Question rephrased: What was the TOTAL number who responded Favorable?

    Statement 1: The number of voters who did not respond favorable for either candidate was 40.
    Since 40 did NOT respond Favorable, the total number who DID respond Favorable = 100-40 = 60.
    SUFFICIENT.

    Statement 2: The number of voters who responded unfavorable for both candidates was 10.

    No way to determine the total number who responded Favorable.
    INSUFFICIENT.

    The correct answer is A.

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    vipulgoyal Master | Next Rank: 500 Posts Default Avatar
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    Post Thu Oct 10, 2013 1:24 am
    Not favorable to both = 40
    Remove overlapping to get either or = 20 + 40 + 35 + 35 - 40 (Both) = 90
    So 90 are those who says not favorable (including Unfavorable or Not sure) to either M or N
    Favorable to both M and N = 100 - 90 = 10
    OA A

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    Post Mon Oct 14, 2013 2:56 am
    For statement 1, it helps to realize that the distinction between "unfavorable" and "not sure" is no longer a real distinction; all that matters is "favorable" or NOT "favorable".

    Once you have that, you can make the usual two-way table for overlapping sets.
    On the columns, "M favorable", "M not favorable", "total".
    On the rows, "N favorable", "N not favorable", "total".

    The information in statement 2 doesn't distinguish in any way between the "favorable" people (in whom we are interested) and the "not sure" people (in whom we aren't).

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