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.
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.
Answer: A
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