Need a Better explanation for DS#134 OG15

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shubh425: Junior | Next Rank: 30 Posts; Posts: 20; Joined: Tue Jan 19, 2016 10:42 pm

by shubh425 » Mon Jun 13, 2016 12:44 am

Please explain the DS Q#134 from OG15.

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Source: Beat The GMAT — Data Sufficiency | Mon Jun 13, 2016 12:44 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Mon Jun 13, 2016 2:13 am

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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