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# M20-20

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Math Expert
Joined: 02 Sep 2009
Posts: 50578

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16 Sep 2014, 00:08
00:00

Difficulty:

5% (low)

Question Stats:

90% (00:51) correct 10% (00:52) wrong based on 143 sessions

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A consumer preference survey revealed that out of the 200 surveyed people 80 liked tea and 70 liked both tea and coffee. If 100 of the surveyed people liked neither tea nor coffee, how many of the surveyed people liked coffee but not tea?

A. 10
B. 20
C. 40
D. 50
E. 60

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Math Expert
Joined: 02 Sep 2009
Posts: 50578

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16 Sep 2014, 00:08
Official Solution:

A consumer preference survey revealed that out of the 200 surveyed people 80 liked tea and 70 liked both tea and coffee. If 100 of the surveyed people liked neither tea nor coffee, how many of the surveyed people liked coffee but not tea?

A. 10
B. 20
C. 40
D. 50
E. 60

Since $$\{Total\}=\{Tea\}+\{Coffee\}-\{Both\}+\{Neither\}$$, then: $$200=80+\{Coffee\}-70+100$$, so $$\{Coffee\}=90$$.

Therefore the number of people who like coffee but not tea is $$\{Coffee\}-\{Both\}=90-70=20$$.

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10 Oct 2017, 04:55
Solve using venn diagrams. The answer is 20 , i.e option B
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Re: M20-20 &nbs [#permalink] 10 Oct 2017, 04:55
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# M20-20

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