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Sets Issue!!

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Sets Issue!! [#permalink] New post 26 Aug 2011, 02:16
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Question Stats:

0% (00:00) correct 100% (02:12) wrong based on 1 sessions
Yes No Unsure
A 500 200 100
B 400 300 100


In a certain survey, each of 800 people expressed their attitude to A & B. They can say yes, no or unsure. If 200 people said yes to A but not to B, how many people said yes to either A or B?

pls help me understand the logic?
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Re: Sets Issue!! [#permalink] New post 26 Aug 2011, 13:24
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DeeptiM wrote:
Yes No Unsure
A 500 200 100
B 400 300 100


In a certain survey, each of 800 people expressed their attitude to A & B. They can say yes, no or unsure. If 200 people said yes to A but not to B, how many people said yes to either A or B?

pls help me understand the logic?



Here you go -
People who said yes to A will comprise of 2 kinds of ppl
- those who said yes to both A & B
- those who said yes to A but no or unsure to B, as per the stem the value of this is 200.

500=200 exclusive +common
=> common (Those who said Yes to both A& B) = 300

Similary for B, the people who said yes to B fall in two categories
- those who said yes to both A& B, this value should be 300 as we calculated from above
- those who said yes to B but no or unsure to A

400=300 common + exclusive to B
=> exclusive to B = 100

Finally,
The people who said yes to either A or B will be equal to :

No of ppl who said yes to exclusively A + No of ppl who said yes to exclusively B + Number of ppl who said yes to both

= 300 + 100 + 200 (from the above calcs)
=600

Ans: 600

so whats the ans?
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Re: Sets Issue!! [#permalink] New post 26 Aug 2011, 13:44
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DeeptiM wrote:
Yes No Unsure
A 500 200 100
B 400 300 100


In a certain survey, each of 800 people expressed their attitude to A & B. They can say yes, no or unsure. If 200 people said yes to A but not to B, how many people said yes to either A or B?

pls help me understand the logic?


This is a question where all we need is:



Yes
A500
B400


We can forget about rest of the columns. Non-GMAT type because usually almost everything has to be used in order to get to the result in a GMAT question.

Here,
200 people said yes to A but not B, or 200 people said YES to ONLY A.

n(Yes to A)=n(Yes to ONLY A)+n(Yes to both A and B)
500=200+n(Yes to both A and B)
n(Yes to both A and B)=500-200=300---------------1

n(Yes to B)=n(Yes to ONLY B)+n(Yes to both A and B)
400=n(Yes to ONLY B)+300 (From 1 above)
n(Yes to ONLY B)=400-300=100

Now,
n(Total Yes)=n(Yes to ONLY A)+n(Yes to ONLY B)+n(Yes to both A and B)
n(Total Yes)=200+100+300=600.

Ans: "600"
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Re: Sets Issue!! [#permalink] New post 26 Aug 2011, 11:48
pls help on this one..
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Re: Sets Issue!! [#permalink] New post 26 Aug 2011, 20:54
+1 to both of you for helping...
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Re: Sets Issue!! [#permalink] New post 26 Aug 2011, 22:22
we were asked to find out Yes for A or B = yes A+ yes B -yes for both A&B =?


Number of people who voted yes for A = Yes for A only + Yes for both A &B

500 = 200 + both yes

=> both yes = 300


=> A+B - A&B = 500+400 - 300 = 600
Re: Sets Issue!!   [#permalink] 26 Aug 2011, 22:22
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