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A market research company surveyed users of the toothpaste industry's

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A market research company surveyed users of the toothpaste industry's [#permalink]

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Question Stats:

57% (01:00) correct 43% (01:08) wrong based on 56 sessions

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A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
[Reveal] Spoiler: OA

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Re: A market research company surveyed users of the toothpaste industry's [#permalink]

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New post 12 Feb 2017, 00:00
ziyuenlau wrote:
A market research company surveyed users of the toothpaste industry's two most popular brands, Brand X and Brand Y. If each person contacted reported that they used at least one of the two brands, what percent of respondents reported that they only use Brand Y?

(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.


Hi..

Info from the Q :- all of the person use ATLEAST one of the brands..

Let's see the statements..


(1) Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was \(3:2\).
we do not know how many use both so insufficient
Say all using brand Y use brand X then 3:2 or 3z:2z would mean that 2z is part of 3z, that is 2z use both and z use ONLY x..
Ans is 0 for Y..
But say none use both, so 2z out of (3z+2z) use Y, thus %=2z/5z *100=40%..
Different answers possible
Insufficient

(2) Among the respondents who reported that they use Brand X, one half also use Brand Y.
So if x use X, then 1/2*x use both, nothing about ONLY y..
Insufficient..

Combined..
3z and 2z is X and Y...
And from II, 3z/2 is common, so total = 3z+2z-3z/2=7z/2..
Only Y =2z-3z/2=z/2..
%=(z/2)/(7z/2) * 100= 100/7%
Suff

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Re: A market research company surveyed users of the toothpaste industry's [#permalink]

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New post 06 Sep 2017, 22:16
The question is asking for the ratio Z
Z = (y-only) / (x-only + y-only + both)

1. "Among the respondents, the ratio of those who reported that they use Brand Y to those who reported that they use Brand X was 3:2"
=> (y-only + both) / ( x-only + both) = 3/ 2
=> both = 2y - 3x
Insuff.

2. "Among the respondents who reported that they use Brand X, one half also use Brand Y."
=> x-only = both
Insuff.

(1+2) => 2y - 3x = x = both
=> y = 2x = both
=> Z = 2x / ( x + 2x + x) = 1/2
C is suff.

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Re: A market research company surveyed users of the toothpaste industry's   [#permalink] 06 Sep 2017, 22:16
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