Data Sufficiency

dhirajdas53 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.