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A data company recently conducted a survey

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A data company recently conducted a survey

by dhirajdas53 » Sun Apr 28, 2013 12:53 am
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
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Source: — Data Sufficiency |

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by Anju@Gurome » Sun Apr 28, 2013 1:11 am
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.
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by gaurav_gaur » Sun Apr 28, 2013 1:12 am
Need to find the number of people who are using product Y

1)65% people replied only product X
the statement is not sufficient as there are number of unknowns like how many people are using both the products or how many are using only Y.
So the statement is not correct.

2)10% people used both the products X and Y.
again there are unknowns here that how many used only X or only Y
This statement is also insufficient.

Combining the 2:
Number of people who use only product X: 65%
Number of people who use both products X & Y: 10%
So the number of people who use only product Y: 25%

But still we need the number of people who have participated in the survey.

So the answer should be E
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by GMATGuruNY » Sun Apr 28, 2013 2:51 am
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
Total = only X + only Y + both.
Thus:
Only Y = total - only X - both.

Statement 1: 65% of the respondents used only product X
Since 65/100 = 13/20, the total number of people must be a multiple of 20.
No way to determine the value of only Y.
INSUFFICIENT.

Statement 2: 10% of survey respondents used both products X and Y
Since 10/100 = 1/10, the total number of people must be a multiple of 10.
No way to determine the value of only Y.
INSUFFICIENT.

Statements combined:
Case 1: Total = 20
Only X = (13/20)(20) = 13.
Both = (1/10)(20) = 2.
Only Y = 20-13-2 = 5.
Here, the total number of people who used product Y = only Y + both = 5+2 = 7.

Case 2: Total = 40
Only X = (13/20)(40) = 26.
Both = (1/10)(40) = 4.
Only Y = 40-26-4 = 10.
Here, the total number of people who used product Y = only Y + both = 10+4 = 14.

Since the total number of people who used product Y can be different values, the two statements combined are INSUFFICIENT.

The correct answer is E.
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by rakhi.agrawal15 » Sun Apr 28, 2013 11:35 am
I always used to think If by combining answer is coming then answer should be C. I never considered if 2 different answers are coming then the information is insufficient. Thanks.
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