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Patio + Swimming poll (sets)

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by 4meonly » Tue Dec 02, 2008 12:14 am
Guys,
please check my thinking


Image
OA B

75 = (have patio)+(have pool)-(have patio and pool)+(do not have patio and pool)
Main stem:
75 = (48)+(have pool)-(have patio and pool)+(do not have patio and pool)
Question: (have pool) = ?

(1)
only patio = 38, therefore (have patio and pool)=10
75 = (38)+(have pool)-(10)+(do not have patio and pool)
Question: (have pool) = ?, we do not know (do not have patio and pool).
INSUFF

(2)
(have patio and pool)=(do not have patio and pool) let it be x
75 = (48)+(have pool)-x+x
75 = (48)+(have pool)
(have pool)=27
SUFF

B


I dont know why, but i fell i am not correct :-(
Fell I became very suspicious :)
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Source: — Data Sufficiency |
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My answer both answer are necessary

by alto34 » Tue Dec 02, 2008 4:49 am
Hi,


Let's simplify the problem:
A= only patio
B= only swimming pool
C= Patio and swimming pool
D= Neither Patio nor Swimming Pool

So

75 = A +B+C+D
48 = A + C

Hence 1: allows us to know that C= 10 so it's insufficient to solve the problem alone

hence 2: alone we can only find that C=D, alone this hence is insufficient

But if you take BOTH hences together you can find the answer:
75 = (A+C) + B + D = (A+C) + B + C = 48 + B + 10
75 = 58 + B

B = 17


PS: To help you solve this problem you can also draw some circles.
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by Spring2009 » Tue Dec 02, 2008 5:24 am
I think using Venn diagram to solve this problem is much clearer and quicker.
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Re: My answer both answer are necessary

by jimmiejaz » Tue Dec 02, 2008 5:48 am
alto34 wrote:Hi,


Let's simplify the problem:
A= only patio
B= only swimming pool
C= Patio and swimming pool
D= Neither Patio nor Swimming Pool

So

75 = A +B+C+D
48 = A + C

Hence 1: allows us to know that C= 10 so it's insufficient to solve the problem alone

hence 2: alone we can only find that C=D, alone this hence is insufficient

But if you take BOTH hences together you can find the answer:
75 = (A+C) + B + D = (A+C) + B + C = 48 + B + 10
75 = 58 + B

B = 17


PS: To help you solve this problem you can also draw some circles.
It will be A+B-C+D
so From 2nd stmt we will get 75 = A+B as (C=D)
A=48, so B=27.
Hence imo B.
What if i have not yet beat the beast, I know i will beat it!!!!!!!!
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by Carloblacksun » Wed Dec 03, 2008 7:25 am
pick numbers to check if B is correct

A = 48

A + B + C + D = 75

C = D

that's all we know

example 1
C = D = 11

then B = 5

C = D = 10

then B = 7

Hence we need statement one to answer... so...C!
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by lunarpower » Fri Dec 05, 2008 3:51 am
this is a canonical overlapping sets problem, so set up the double-set matrix.

a solution is here:
https://xs228.xs.to/xs228/08263/pool_pat ... ion565.jpg

answer = b

--

if you don't like using x for the number quoted in statement (2), you could always try plugging in a couple of different numbers, and noting that you get the same answer no matter what number you plug in.
Ron has been teaching various standardized tests for 20 years.

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