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

+ A

................................ Brand X................ Brand Y.............Total

First Month................... x...........................y....................100

Second Month.......... 0.9x+0.4y...........0.6y + 0.1x..........100

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

Second month Brand Y = 0.6*.5*Total + 0.1*0.5*Total = 0.35*Total
35% shoppers bought Brand Y in the second month. Sufficient

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

Total number of shoppers is irrelevant. We just need the percentage of shoppers who buy brand Y.

Answer (A)
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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.

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

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

Hi VeritasKarishma

I solved this question using the Matrix based approach. However, after solving this question one thing raised on my mind.
The question stem says, "each shopper bought one of two brands of detergent, X or Y".

Therefore, there cannot be some number of people who bought both brands of X and Y correct?

What would the phrase look like if there were some number of people who bought both brands of X and Y?
I am asking this because while solving this question I wasted some time as I did go through these questions.

Thank you.

This was very easy to answer in matrix method.

Please refer attached

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The question tells you that the shoppers bought one of the two brands. So they bought only one.
Had the question said 'at least one of the two brands' that would mean they bought 1 or both. Usually, people can belong to multiple sets until and unless specified otherwise (as done in our question).
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(1) In the first month, 50 percent of the shoppers bought Brand X. : this tells us rest 50 % bought Y in the first month and the stem tells us that 60% of people who bought Y in first month bought Y in second month as well, and that's exactly what's asked.

No of people who bought Y in second month= 60% of 50%

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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