OG 12, tough sets DS

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vkb16: Master | Next Rank: 500 Posts; Posts: 122; Joined: Mon Dec 15, 2008 12:03 am; Thanked: 2 times

OG 12, tough sets DS

by vkb16 » Wed Oct 21, 2009 12:42 am

favourable Unfavourable Not sure
Candidate M 40 30 40
Candidate N 30 35 35

The table above shows the results of a survey of 100 voters who each responded ''Favourable'' or Unfavourable, or Not Sure when asked about their impressions of Candidate M and N.
What was the number of voters who responded 'Favourable' for Both candidates?

I. The no. of voters who did not respond 'favourable' for either candidate was 40

II. the no. of voters who responded 'unfavourable' for both candidates was 10.

OA is A

the og explanation is quite complicated.. does someone have a simpler approach? Experts pls help!!

thanks

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Source: Beat The GMAT — Data Sufficiency | Wed Oct 21, 2009 12:42 am

Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pm; Location: Toronto; Thanked: 539 times; Followed by:164 members; GMAT Score:800

by Testluv » Wed Oct 21, 2009 11:35 pm

Hi vkb16,

remember there are 100 people.

From the table, we know that 40 voted favorably for candidate M and 30 voted favorably for candidate N.
Therefore, 70 voted favorably for at least one of them (M or N), right?

But statement 1 tell us 40 didn't vote favorably for either of them. But 70 + 40 is 110 (not 100!).

So what's going on? Simple. 10 people voted for BOTH M and N: an overlap.

Statement 1 is sufficient.

Think about it this way. Let's say you wanted to count the number of kids in a school. Let's say there were 40 kids in Math class, and 30 in English class. If you add the two you have 70.

But let's say Billy is in both class. woops! You would have counted Billy twice: once in the count of Math students, and again in the count of English students. So, in order to arrive at the total number of kids in the school, you would have to subtract those who are in both classes (and assume there aren't any other classes). There is a counting formula that comes out of all of this:

Total= Number in Group 1 + Number in Group 2-Number in BOTH Groups

Now let's say there are other kids in the school but they are not in Math class and they are not in English class. Well, obviously, you will have failed to count them. Then the formula becomes:
Total= #in Group 1 + # in Group 2 - # in BOTH + # in Neither.

Applied to this problem, you have:
Total = Number favorable for at least one - Number favorable for both (don't wanna double count) + the number who did NOT vote favorable for either (haven't counted them yet, and these people can be in either the "unfavorable" or the "not sure" cateory)

plugging in:

100 = (40+30)-Both + 40

And, obviously, because it is data sufficiency, you wouldn't actually solve for "both". In fact, because it is data sufficiency, you shouldn't even set up the equation--the moment you see you can set it up, and that it has only one unknown variable IS the moment you know it is sufficient.

From statement 2, we know that 10 responded unfavorably for both. These people would definitely go into the last variable in our formula--the number who did NOT vote favorably for either. But that variable includes both the people who responded "unfavorable" and the people who responded "not sure". And we don't have enough information to quantify the possible overlaps in those sets. So we still have two undetermined variables in our equation. Not sufficient.

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life is a test: Master | Next Rank: 500 Posts; Posts: 138; Joined: Mon Mar 02, 2009 12:02 pm; Thanked: 15 times

Re: OG 12, tough sets DS

by life is a test » Thu Oct 22, 2009 11:16 pm

vkb16 wrote:
the og explanation is quite complicated.. does someone have a simpler approach? Experts pls help!!

thanks

Normally such qs can be easily calculated using venn diags but in this case the difficult part was figuring out how the different quadrants are split...hope the attached helps.

Attachments

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samrat chatterjee: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Oct 14, 2009 11:04 am

just a doubt...

by samrat chatterjee » Thu Oct 22, 2009 11:49 pm

If we consider only for Candidate M(total=100)

Fav NFav Nsure
M 40 30 40

I assumed Fav NFav and Nsure are complementary to each other.

If 40 favor, 60 remain. Out of these 60 if 30 are Nfav then only remaining 30 can be Nsure(but this figure is projected as 40 in the problem)... can someone clearify....

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pm; Location: Toronto; Thanked: 539 times; Followed by:164 members; GMAT Score:800

by Testluv » Fri Oct 23, 2009 1:12 am

Hi Samrat,

Statement 1 gives us information about those who did NOT respond favorably. If they did not respond "favorably", then either they responded "unfavorably" or else they responded "not sure". It sounds like you might be incorrectly equating not responding "favorably" to responding "unfavorably".[/quote]

Kaplan Teacher in Toronto

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samrat chatterjee: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Oct 14, 2009 11:04 am

hello and thankyou...

by samrat chatterjee » Fri Oct 23, 2009 1:46 am

I did not go as far as the statement1 .. i am talking about the main data which states

M 40 30 40

is this correct???
i think it should be
M 40 30 30

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Testluv: GMAT Instructor; Posts: 1302; Joined: Mon Oct 19, 2009 2:13 pm; Location: Toronto; Thanked: 539 times; Followed by:164 members; GMAT Score:800

by Testluv » Fri Oct 23, 2009 1:49 am

Hi Samrat,

actually, I think I see your mistake now. You confused because the sum of 40, 30 and 40 is 110, and right you should be. The original poster erred. The actual numbers are 40, 20 and 40 (it's question #124 on page 284 of OG12). (I didn't notice b/c I am familiar with the problem, and also because not noticing the original poster's mistake, incidentally, does not preclude solving the problem properly).

Kaplan Teacher in Toronto