A marketing firm determined that, of 200 households : PS Archive
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# A marketing firm determined that, of 200 households

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VP
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A marketing firm determined that, of 200 households [#permalink]

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25 Dec 2005, 23:34
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A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

(A) 15
(B) 20
(C) 30
(D) 40
(E) 45

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Senior Manager
Joined: 14 Apr 2005
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25 Dec 2005, 23:51
TeHCM wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

(A) 15
(B) 20
(C) 30
(D) 40
(E) 45

I get 15.

Only A + only B + A and B = 120
Given that only B = 3 (A and B)
Substituting we get A and B = 15.
SVP
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25 Dec 2005, 23:55
TeHCM wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

(A) 15
(B) 20
(C) 30
(D) 40
(E) 45

A. 15.

total = 200
Not A nd B = 80
A = 60
Remaining = B + (A and B) = 60
B = 3 (A and B)
B + (A and B) = 60
3 (A and B) + (A and B) = 60
4 (A and B) = 60
A and B = 15
Senior Manager
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27 Dec 2005, 12:09
IMO should be 30.

ALL=A+B-AB+NEITHER
200=60+3X-X+80
X = 30

Where did I go wrong ?
SVP
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27 Dec 2005, 13:57
I also get C.

60 + 3X + 80 - X = 200
2X = 60
X = 30

Look like I am missing something.
Director
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29 Dec 2005, 10:35
TeHCM wrote:
A marketing firm determined that, of 200 households surveyed, 80 used neither Brand A nor Brand B soap, 60 used only Brand A soap, and for every household that used both brands of soap, 3 used only Brand B soap. How many of the 200 households surveyed used both brands of soap?

120 uses Brand A, Brand B or both..

60 uses Brand A..

out of other 60.. x +3x = 60 x = 15.
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Director
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29 Dec 2005, 10:36
hkm_gmat wrote:
IMO should be 30.

ALL=A+B-AB+NEITHER
200=60+3X-X+80
X = 30

Where did I go wrong ?

i got the same answer. .read the question again. .for every household that used both the brands, 3 households use Brand B
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29 Dec 2005, 10:36
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