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

Question

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%

LipiSinha · Accepted Answer

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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TarunKumar1234 · Answer

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.

twobagels · Answer

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

Bunuel · Answer

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. https://gmatclub.com/forum/download/file.php?id=60029 2021-01-12_00-55-38.png

pierjoejoe · Answer

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

liberoaut · Answer

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?

My god, this wording is so devious. It reads as if (B&!A : 3(A&B & A&!B)) or (B&!A : 1/3(A&B & A&!B)), super unclear. As a result all the answers I was getting did not exist. Are all GMAT problems going to be like this?

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

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