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# 30 people are currently sitting in a coffee shop in Brooklyn. 20 peopl

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Math Expert
Joined: 02 Sep 2009
Posts: 54462
30 people are currently sitting in a coffee shop in Brooklyn. 20 peopl  [#permalink]

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15 Aug 2017, 01:11
1
1
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Question Stats:

90% (00:58) correct 10% (01:38) wrong based on 95 sessions

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30 people are currently sitting in a coffee shop in Brooklyn. 20 people have a beard and 18 people are wearing a t-shirt. If 4 people have neither a beard nor a t-shirt, how many people have both a beard and a t-shirt?

A. 6
B. 8
C. 10
D. 12
E. 14

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Re: 30 people are currently sitting in a coffee shop in Brooklyn. 20 peopl  [#permalink]

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15 Aug 2017, 01:35
Bunuel wrote:
30 people are currently sitting in a coffee shop in Brooklyn. 20 people have a beard and 18 people are wearing a t-shirt. If 4 people have neither a beard nor a t-shirt, how many people have both a beard and a t-shirt?

A. 6
B. 8
C. 10
D. 12
E. 14

Let the # of people with only Beard = a
Let the # of people with both beard and tshirt = b
Let the # of people with only tshirt = c

a+b+c=26 (30-4)
a+b=20
b+c=18

=> 20+c=26 =>c=6
=> b+6=18 =>b=12

Thus, Answer=D
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Re: 30 people are currently sitting in a coffee shop in Brooklyn. 20 peopl  [#permalink]

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18 Aug 2017, 09:15
1
Bunuel wrote:
30 people are currently sitting in a coffee shop in Brooklyn. 20 people have a beard and 18 people are wearing a t-shirt. If 4 people have neither a beard nor a t-shirt, how many people have both a beard and a t-shirt?

A. 6
B. 8
C. 10
D. 12
E. 14

We can use the following formula:

Total people = # with beard + # with T-shirt - # with both + # with neither

30 = 20 + 18 - b + 4

30 = 42 - b

b = 12

Answer: D
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Re: 30 people are currently sitting in a coffee shop in Brooklyn. 20 peopl   [#permalink] 18 Aug 2017, 09:15
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# 30 people are currently sitting in a coffee shop in Brooklyn. 20 peopl

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