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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In a two-month survey of shoppers, each shopper bought one o
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Anaira Mitch
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Statement 1: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.
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.
The correct answer is A.
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Thanks Mitch.
GMATGuruNY wrote:Statement 1: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.
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.
The correct answer is A.
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Solution:Anaira Mitch wrote: ↑Thu Mar 22, 2018 10:25 pmIn 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.
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.
Answer: A
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