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

Re: PS: MarKeting Firm [#permalink]
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.

Re: PS: MarKeting Firm [#permalink]
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

Re: PS: MarKeting Firm [#permalink]
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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