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

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

by Anaira Mitch » Thu Mar 22, 2018 10:25 pm
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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by Anaira Mitch » Sat Mar 24, 2018 7:21 pm
Ny1?

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by GMATGuruNY » Sun Mar 25, 2018 2:42 am
Anaira Mitch 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.
Statement 1:
Let the total number of shoppers in the first month = 100, implying 50 X-shoppers and 50 Y-shoppers.
Since 90% of the 50 shoppers in red repurchased X in the second month, the red group in the second month yields 45 X-shoppers and 5 Y-shoppers.
Since 60% of the 50 shoppers in blue repurchased Y in the second month, the blue group in the second month yields 30 Y-shoppers and 20 X-shoppers.
Thus:
(total Y-shoppers in the second month)/(total shoppers) = (5 + 30)/100 = 35/100 = 35%.
SUFFICIENT.

Statement 2:
No information about the percentage of Y-shoppers in the second month.
INSUFFICIENT.

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by Anaira Mitch » Sun Mar 25, 2018 5:00 am
Thanks Mitch.
GMATGuruNY wrote:
Anaira Mitch 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.
Statement 1:
Let the total number of shoppers in the first month = 100, implying 50 X-shoppers and 50 Y-shoppers.
Since 90% of the 50 shoppers in red repurchased X in the second month, the red group in the second month yields 45 X-shoppers and 5 Y-shoppers.
Since 60% of the 50 shoppers in blue repurchased Y in the second month, the blue group in the second month yields 30 Y-shoppers and 20 X-shoppers.
Thus:
(total Y-shoppers in the second month)/(total shoppers) = (5 + 30)/100 = 35/100 = 35%.
SUFFICIENT.

Statement 2:
No information about the percentage of Y-shoppers in the second month.
INSUFFICIENT.

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### Re: In a two-month survey of shoppers, each shopper bought one o

by [email protected] » Fri Jun 11, 2021 8:58 am
Anaira Mitch wrote:
Thu Mar 22, 2018 10:25 pm
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.
Solution:

We need to determine the percentage of the shoppers that bought Brand Y in the second month. If we let T be the total number of shoppers in the survey and x be the number of shoppers who bought brand X detergent in the first month, then the number of shoppers who bought Brand Y detergent in the second month is:

0.1x + 0.6(T - x)

Note that 0.1x is the number of shoppers who bought Brand X in the first month but switched to Brand Y in the second month and 0.6(T - x) is the number of shoppers who bought Brand Y in the first month and continued to buy Brand Y in the second month.

If we can determine the values of T and x, then we can determine the number of shoppers who bought Brand Y in the second month and hence the percentage of shoppers who bought Brand Y detergent in the second month.

Statement One Alone:

This means x = 0.5T. Thus the expression in the our stem analysis simplifies to:

0.1(0.5T) + 0.6(T - 0.5T) = 0.05T + 0.3T = 0.35T

Although we don’t know the value of T, the expression 0.35T really means that 35% of the total number of shoppers bought Brand Y in the second month. Statement one alone is sufficient.

Statement Two Alone:

This means T = 5,000. Thus the expression in the our stem analysis simplifies to:

0.1x + 0.6(5000 - x)

However, without knowing the value of x, we can’t determine the number of shoppers who bought Brand Y in the second month, and hence we can’t determine the percentage of shoppers who bought Brand Y in the second month. Statement two alone is not sufficient.

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