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30% of consumers like only product A, and for every consumer that like

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Bunuel
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30% of consumers like only product A, and for every consumer that like [#permalink] 30% of consumers like only product A, and for every consumer that like   11 Jan 2021, 13:53
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A
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E

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45% (medium)

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71% (02:12) correct 29% (02:45) wrong based on 267 sessions
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30% of consumers like only product A, and for every consumer that likes only product B, 3 also like product A. If 18% of consumers like neither product, what percentage likes both?

A. 13%
B. 18%
C. 26%
D. 30%
E. 39%
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E
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TarunKumar1234
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Re: 30% of consumers like only product A, and for every consumer that like [#permalink] 30% of consumers like only product A, and for every consumer that like   11 Jan 2021, 14:38
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Let's say total consumers = 100

So, Only A= 30, Only B = x (say) then n(A∩B) = 3*x and n(AUB) = 100-18= 82

Now, n(AUB) = only n(A) + only n(B)+ n(A∩B)
or, 82= 30+x+ 3x or, x= 52/4= 13

So, n(A∩B) = 3*x = 3*13= 39, I think E. :)
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Re: 30% of consumers like only product A, and for every consumer that like [#permalink] 30% of consumers like only product A, and for every consumer that like   11 Jan 2021, 15:49
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I picked a number to work with, 1000.

From the question stem, 300 only like A.
3x like A and B.
x like only B.
180 like neither.

1000 = 300 + x + 3x +180

x = 130
Answer is 3x = 390, which is 390/1000 = 39%

Ans. E
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Re: 30% of consumers like only product A, and for every consumer that like [#permalink] 30% of consumers like only product A, and for every consumer that like   11 Jan 2021, 20:01
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Let no. Of consumers be 100.
Those who like only A = 30
Let, those who like only B be x
So, those who like both B and A = 3x.

Only A + Only B + Both + Neither = 100
30+x+3x+18 = 100
4x = 52
x = 13
3x = 39

Therefore, required percentage = 39%

The answer will be E.

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Re: 30% of consumers like only product A, and for every consumer that like [#permalink] 30% of consumers like only product A, and for every consumer that like   19 Jan 2021, 02:00
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Bunuel
30% of consumers like only product A, and for every consumer that likes only product B, 3 also like product A. If 18% of consumers like neither product, what percentage likes both?

A. 13%
B. 18%
C. 26%
D. 30%
E. 39%

Veritas Prep Official Explanation



Draw out the diagrams, paying special attention to the ratio wording (for every consumer that likes B only, 3 like both). Since 48 of the 100 consumers are accounted for by only A and NEITHER, then 3x + x must equal 52. 4x = 52 and x = 13, so 3x = 39. Both = 39% consumers.



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Re: 30% of consumers like only product A, and for every consumer that like [#permalink] 30% of consumers like only product A, and for every consumer that like   24 Sep 2024, 07:41
A - A&B = 30
thus
A = 30 + A&B
the second one is

(B-A&B)/A&B = 1/3
B = 4/3 A&B
because for everyone who likes product be only (B-A&B), there are 3 who likes B and also A (A&B)

we know that
100 = A + B - A&B +NONE = 30 + A&B + 4/3 A&B - A&B + 18

52 = 4/3 A&B --> A&B = 39
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Re: 30% of consumers like only product A, and for every consumer that like [#permalink]
24 Sep 2024, 07:41
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Bunuel
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