Data Sufficiency

BTGmoderatorDC wrote: ↑

Wed Aug 05, 2020 5:21 pm

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

OA E

Source: Veritas Prep

Say the p no. of people were surveyed, x no. of people used only product X, y no. of people used only product Y, and n no. of people used both the products.

Thus, we have

p = x + y + b

=> y + b = no. of people who use product Y. We have get the value of y + b.

Let's take each statement one by one.

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

=> p = 65% of p + (y + b)
=> y + b = 0.35p. Since we do not know the value of p, we can't get the answer. Insufficient.

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

=> b = 10% of p = 0.1p

Certainly insufficient.

(1) and (2) together

Even with y + b = 0.35p. and b = 0.1p, we can't get the unique value of y + b. Insufficient.

Correct answer: E

Hope this helps!

-Jay
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