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Tough Overlapping sets

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Tough Overlapping sets

by abhi75 » Sat May 03, 2008 10:32 am

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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.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Can someone please explain how to solve this kind of problems. If the table is not clear please refer to the attached document.

Thanks in advance.
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Source: — Data Sufficiency |

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Re: Tough Overlapping sets

by lunarpower » Thu May 08, 2008 12:42 am

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explanation on the image (link attached)

the orange and blue are no accident. go gators!

click here to see the solution

[editor: this link is broken - for an updated link, see below.]
Last edited by lunarpower on Mon Nov 16, 2009 2:37 am, edited 1 time in total.
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by abhi75 » Fri Jun 13, 2008 6:43 am

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Hey Ron,

Thanks a lot for the solution. I really appreciate it.

-A
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by lunarpower » Fri Jun 13, 2008 10:42 am

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no problem - i'm glad you found it useful. that is a cool problem.
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by lunarpower » Sun Jun 15, 2008 4:59 pm

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lunarpower wrote:no problem - i'm glad you found it useful. that is a cool problem.
haha, i just realized i posted the wrong answer on the solution sheet.

the reasoning is all correct, but the answer is supposed to be 'a'

just testing you guys.
really.
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by lunarpower » Mon Nov 16, 2009 2:35 am

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here's an updated link

https://www.postimage.org/image.php?v=gx1ffBD9

the answer still mistakenly says 'B' on the bottom of the page. (it's supposed to be (a))
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by OneTwoThreeFour » Sat Jan 01, 2011 12:58 pm

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Great solution! But wouldn't it be helpful just to create a triple matrix in the beginning? I don't think two minutes is enough time to make two separate tables. Thanks a lot I was having a lot of trouble with this one!
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by lunarpower » Sat Jan 01, 2011 1:48 pm

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OneTwoThreeFour wrote:Great solution! But wouldn't it be helpful just to create a triple matrix in the beginning? I don't think two minutes is enough time to make two separate tables. Thanks a lot I was having a lot of trouble with this one!
well -- no matter what approach you take, you should always make separate matrices for statements (1) and (2) -- even if the row and column headings are the same (which they usually will be).
the reason is simple: statement (1) contains information that's not in statement (2), and statement (2) also contains information that's not in statement (1). if you try to do all of this in one matrix, the potential for confusion is way too high, especially because you have to write on plastic with a marker (no pencils or erasers!).

if you want to make the full-on Favorable/Unfavorable/Not Sure matrix for statement (1), you can do so.
if you do this, instead of a simple "40" in the "not favorable" row (which encompasses both "unfavorable" and "not sure"), you'll have an "x" and a "40 - x", respectively, in separate rows for "unfavorable" and "not sure" (or vice versa). overall, the problem will still work out the same way, though -- if you do the algebra through the rest of the table, you'll notice that all of the x's cancel out of the square that you want.
still, though, it's good to be able to recognize that you don't have to consider any distinctions other than "favorable"/"not favorable" in that problem, though -- this sort of recognition is the linchpin of several other problems with multiple distinctions between items, too. for example, see problem #107 in the OG12 data sufficiency section.
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by OneTwoThreeFour » Sat Jan 08, 2011 11:01 am

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I understand. I was thinking by creating one triple matrix in the beginning, and if only part A is sufficient, then you can just black out your numbers and eliminate B, C, E and move on to statement 2. You can then fill out the table with the remaining spaces left in the table when analyzing statement 2. However if statement 1 one is insufficient, statement 2 is insufficient, and only the combined statements of 1 & 2 are sufficient, then the table would get a lot messier with all the blacked out numbers. So in the end, I guess your strategy is the more efficient one. Anyways, thank you so much for replying back to me and I sincerely appreciated your input.
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by GMATGuruNY » Sat Jan 08, 2011 3:38 pm

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abhi75 wrote: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.


Thanks in advance.
I wouldn't do much math for this problem. We're looking for the number who voted favorable for both M and N. In other words, the overlap between the 2 favorable groups.

The big idea with overlapping group problems is to subtract the overlap. When we count the number who voted favorable for M and the number who voted favorable for N, the number who voted favorable for both -- the overlap -- gets counted twice. So that we don't double-count the overlap, it must be subtracted from the total:

Total favorable = Favorable for M + Favorable for N - Favorable for Both

Since we know that 40 voted favorable for M and that 30 voted favorable for N, to solve for the number who voted favorable for both -- the overlap -- we need to know the total number of favorable votes.

Statement 1:
If 40 did not respond favorable for either candidate, then the total who did respond favorable was 100-40 = 60.
60 = 40 + 30 - both.
Both = 10.
Sufficient.

Statement 2:
Tells us the overlap between the 2 unfavorable groups. Doesn't help us to determine the overlap between the 2 favorable groups.
Insufficient.

The correct answer is A.
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by helloanupam » Thu Nov 10, 2011 8:47 am

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Dear Ron,
Turtle speed if you want to call that...but my lack of understanding is the below point in your sheet-

Statement 2 actually does distinguish between the two not favorable cases....HOW? How is this apparent. Please help clarify.
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by vikram.sumer » Tue Apr 24, 2012 12:19 am

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This is a classic kick as* approach. Simple solution to a problem which seems very tough.

Kudos !!
GMATGuruNY wrote:
abhi75 wrote: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.


Thanks in advance.
I wouldn't do much math for this problem. We're looking for the number who voted favorable for both M and N. In other words, the overlap between the 2 favorable groups.

The big idea with overlapping group problems is to subtract the overlap. When we count the number who voted favorable for M and the number who voted favorable for N, the number who voted favorable for both -- the overlap -- gets counted twice. So that we don't double-count the overlap, it must be subtracted from the total:

Total favorable = Favorable for M + Favorable for N - Favorable for Both

Since we know that 40 voted favorable for M and that 30 voted favorable for N, to solve for the number who voted favorable for both -- the overlap -- we need to know the total number of favorable votes.

Statement 1:
If 40 did not respond favorable for either candidate, then the total who did respond favorable was 100-40 = 60.
60 = 40 + 30 - both.
Both = 10.
Sufficient.

Statement 2:
Tells us the overlap between the 2 unfavorable groups. Doesn't help us to determine the overlap between the 2 favorable groups.
Insufficient.

The correct answer is A.
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by ProGMAT » Mon May 05, 2014 9:27 am

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GMATGuruNY wrote: Statement 1:
If 40 did not respond favourable for either candidate, then the total who did respond favorable was 100-40 = 60.
60 = 40 + 30 - both.
Both = 10.
Sufficient.

Statement 2:
Tells us the overlap between the 2 unfavorable groups. Doesn't help us to determine the overlap between the 2 favorable groups.
Insufficient.

The correct answer is A.
If 40 did not respond favourable for either candidate

Silly question, but how 40?
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by GMATGuruNY » Mon May 05, 2014 8:03 pm

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ProGMAT wrote:
If 40 did not respond favourable for either candidate

Silly question, but how 40?
Statement 1 states that the number of voters who did not respond favorable for either candidate was 40.
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by ProGMAT » Mon May 05, 2014 10:55 pm

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GMATGuruNY wrote:
ProGMAT wrote:
If 40 did not respond favourable for either candidate

Silly question, but how 40?
Statement 1 states that the number of voters who did not respond favorable for either candidate was 40.
OMG.. I think I need some sleep.
Thanks Guru
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