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In a two-month survey of shoppers, each shopper bought one of two bran

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In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 19 Jul 2017, 14:20
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  45% (medium)

Question Stats:

74% (02:10) correct 26% (02:11) wrong based on 403 sessions

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In a two-month survey of shoppers, each shopper bought one of two brands of detergent, X or Y, in the first month and again bought one of these brands in the second month. In the survey, 90 percent of the shoppers who bought Brand X in the first month bought Brand X again in the second month, while 60 percent of the shoppers who bought Brand Y in the first month bought Brand Y again in the second month. What percent of the shoppers bought Brand Y in the second month?

(1) In the first month, 50 percent of the shoppers bought Brand X.

(2) The total number of shoppers surveyed was 5,000.
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Re: In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 19 Jul 2017, 14:44
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Re: In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 19 Jul 2017, 15:29
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Leo8 wrote:
+ A


I solved it similar to you and also went with (A). However, I got 35% for the shoppers that bought Brand Y in the second month. I realize that doesn't matter because it is a DS question. But, I've attached my work to show anyone who is curious. As for statement (2), I concur.
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In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 20 Jul 2017, 05:57
moonwalking wrote:
In a two-month survey of shoppers, each shopper bought one of two brands of detergent, X or Y, in the first month and again bought one of these brands in the second month. In the survey, 90 percent of the shoppers who bought Brand X in the first month bought Brand X again in the second month, while 60 percent of the shoppers who bought Brand Y in the first month bought Brand Y again in the second month. What percent of the shoppers bought Brand Y in the second month?

(1) In the first month, 50 percent of the shoppers bought Brand X.

(2) The total number of shoppers surveyed was 5,000.


this question reminds me overlapping sets:)

90% bought X
60% bought y
statement 1 says 50 percent of the shoppers bought Brand X.
which means that out of 90 percent who bought both x and y, only 50% bought x
hence: 90-50 = 40 % :) so I chose A

please, correct if I am wrong :)
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Re: In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 26 Jul 2017, 15:20
Ans A:

St 1: Assume Total Participants in the survey be 100.

First Month: 50% bought brand X. Therefore, Purchase split X=50 and Y=50

Second Month: Revised Purchase split
X= (0.9x50) + (0.4x50) = 65
Y= 100 - 65 = 35%

St 2: Insufficient, as we require the split between X and Y and not the absolute number of buyers
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Re: In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 29 Aug 2017, 02:42
Ans is A:
_________________________1st_____________________2nd
X________________________x______________________0.9x_____1.9x
Y________________________y______________________0.6y______1.6y
__________________________________________________________100

1.9x+1.6y=100
also

1) given x = 50% means 50 out of 100
therefore other y can be calculated
ans can be A/D
2) given total is 5000 in place of 100 therefore we still have 2 variables with us and no solution possible.... D is rejected
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Re: In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 16 Dec 2017, 00:40
I solved the question correctly, but I'm not sure if my understanding below is correct or not. Can someone help...;)
What we know: P(X1)*P(X2) = 90% and P(Y1)*P(Y2)=60%
Question: What perccent of the shoppers bought Brand Y in the second month?
(1) P(X1) = 50% → P(Y1) = 1-P(X1) = 50% → P(Y2) = 60% / 50% = 1.2% → sufficient
(2) Insufficient
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Re: In a two-month survey of shoppers, each shopper bought one of two bran  [#permalink]

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New post 16 Dec 2017, 02:21
dave13 wrote:
moonwalking wrote:
In a two-month survey of shoppers, each shopper bought one of two brands of detergent, X or Y, in the first month and again bought one of these brands in the second month. In the survey, 90 percent of the shoppers who bought Brand X in the first month bought Brand X again in the second month, while 60 percent of the shoppers who bought Brand Y in the first month bought Brand Y again in the second month. What percent of the shoppers bought Brand Y in the second month?

(1) In the first month, 50 percent of the shoppers bought Brand X.

(2) The total number of shoppers surveyed was 5,000.


this question reminds me overlapping sets:)

90% bought X
60% bought y
statement 1 says 50 percent of the shoppers bought Brand X.
which means that out of 90 percent who bought both x and y, only 50% bought x
hence: 90-50 = 40 % :) so I chose A

please, correct if I am wrong :)


Statement 1 means, in 1st pickt 50 choose X and in 2nd pick out of those 50, 90% chose X again while 10 % chose y. Similarly 1st round 50 chose y, 2nd round 60% from those 50 chose Y again and 40 % went with X in 2nd round.
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Re: In a two-month survey of shoppers, each shopper bought one of two bran &nbs [#permalink] 16 Dec 2017, 02:21
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