A data company recently conducted a survey to determine wh

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A data company recently conducted a survey to determine whether people use product X or product Y. If fewer than 100 people were surveyed and each person used either one product or both, how many people used product Y?

(1) 65% of survey respondents used only product X

(2) 10% of survey respondents used both products X and Y

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked

Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked

Both statements (1) and (2) TOGETHER are sufficient to answer the question asked; but NEITHER statement ALONE is sufficient

EACH statement ALONE is sufficient to answer the question asked

Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed
Source: — Data Sufficiency |

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by Anju@Gurome » Sun Apr 28, 2013 9:09 am
varun289 wrote:A data company recently conducted a survey to determine whether people use product X or product Y. If fewer than 100 people were surveyed and each person used either one product or both, how many people used product Y?

(1) 65% of survey respondents used only product X
(2) 10% of survey respondents used both products X and Y
For two overlapping sets, total = number of elements in 1st set + number of elements in 2nd set - number of elements that are in both set + number of elements that are in none of the sets

So, total number of people surveyed (T) = number of people using X (X) + number of people using Y (Y) - number of people using both (B) + number of number of people using none (N)

Here, T < 100 and N = 0
So, T = X + Y - B
We need to determine Y

As the statements provide percentages only not the exact number, there is a pretty good chance that if a certain set of values of X, Y, B, and T satisfy the given equation, their multiples will also satisfy it.
Consider the following two cases,
  • #1. T = 20, X = 15, Y = 7, B = 2
    Number of people using only X = (X - B) = (15 - 2) = 13 = 65% of 20
    Number of people using both = B = 2 = 10% of 20

    #2. T = 40, X = 30, Y = 14, B = 4
    Number of people using only X = (X - B) = (30 - 4) = 26 = 65% of 40
    Number of people using both = B = 4 = 10% of 40
Both of the above cases, satisfy both the statements, but the value of Y are different in each cases.
So, both statements together are also not sufficient.

The correct answer is E.
Anju Agarwal
Quant Expert, Gurome

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