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# M20-20

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Math Expert
Joined: 02 Sep 2009
Posts: 53709

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16 Sep 2014, 01:08
00:00

Difficulty:

5% (low)

Question Stats:

92% (00:51) correct 8% (00:44) wrong based on 153 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: 53709

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16 Sep 2014, 01:08
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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Senior Manager
Joined: 08 Jun 2015
Posts: 426
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38
GPA: 3.33

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10 Oct 2017, 05:55
Solve using venn diagrams. The answer is 20 , i.e option B
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Manager
Joined: 30 Oct 2018
Posts: 58

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01 Dec 2018, 04:27
total -neither = tea + coffee - both
200-100 = 80 +c - 70
c=90
only c = 90 - both
=20 (B)
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Re: M20-20   [#permalink] 01 Dec 2018, 04:27
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# M20-20

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