A data company recently conducted a survey to determine wh

Question

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

(1) 65% of survey respondents used only product X
(2) 10% of survey respondents used both products X and Y

Bunuel · Answer

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

Given: {Total} < 100 and {Neither} = 0.

{Total} = {Only X} + {Only Y} + {Both} . Notice that this formula is different from  {Total} = {X} + {Y} - {Both} .

(1) 65% of survey respondents used only product X. 65%=65/100=13/20, thus {Total} must be a multiple of 20. Not sufficient.

(2) 10% of survey respondents used both products X and Y. 10%=1/10, thus {Total} must be a multiple of 20. Not sufficient.

(1)+(2) If  {Total} = 20 , then  {Only X} = 13/20*20 = 13 , thus  {Y} = {Total} - {Only X} = 7  BUT  {Total} = 40 , then  {Only X} = 13/20*40 = 26 , thus  {Y} = {Total} - {Only X} = 14 . Not sufficient.

Answer: E.

Hope it's clear.

Bluelagoon · Answer

Just pick good numbers to fill in the answers , lets say 80 or 60. Each time with the given fact you will get a different answer.Hence E.

GMAT40 · Answer

Given less than 100 people were surveyed
St 1. X = less than 65 Does not tell anything about Y Not-Suff
St. 2 Both = less than 10 - Not Suff

Together : Can be multiple ans for Y

Ans : E

raj077 · Answer

Another way to look at this question . Total given is a range.Total can be any number from 1 to 99 ( total <100).
(1) X is 65% of Total => X can have multiple values as total is not fixed => Not Sufficient .Unable to get a single value for Y
(2)Both X & Y = 10% of Total => multiple values => Not Sufficient .Unable to get a single value for Y

(1) & (2) together also does not help to get a single value for Y.Hence answer is E

Asifpirlo · Answer

it's a one line solution problem.
we know just one thing and it's less than 100 people, 1 to 99 anything . 99cases not only double cases..
so its not possible to evaluate how many people used Y or X or anything else, just by using % .
so (E)

thatgmat · Answer

I'd disagree with the suggested answer.

The answer should actually be A.

The question asks how many people use Y, not 'only' Y. So it should be the total of the # people who use only Y + the # of people who use Y and X.

If 65% of respondents used only X. And less than 100 people were surveyed, we know that the number of people who used only X must be a variable of a factor of 65 since only whole people (integers) can fit into a bucket.

Since every responder must choose one or both products and neither is not an option we know that 35% use Y.

65 and 35 are both only divisible by 5. Therefore 13 people use only X and 7 use Y or both. Therefore the answer should be A as we can determine the value is 7.

Let me know your thoughts please!

Bunuel · Answer

That's not correct. The answer is E, not A. Examples proving that are given here: a-data-company-recently-conducted-a-survey-to-determine-wh-154001.html#p1233744 Consider the following cases: {Only X} = 13 {Only Y} = 5 {Both} = 2 {Total} = {Only X} + {Only Y} + {Both} = 20 {Only X} = 26 {Only Y} = 10 {Both} = 4 {Total} = {Only X} + {Only Y} + {Both} = 40 Hope it helps.

LinaNY · Answer

Bunuel,

what's the difference between the two formulas? when would we use the second one?
thanks

Bunuel · Answer

The two formulas are:

{Total} = {X} + {Y} - {Both} + {Neither}

Now, since {X} = {Only X} + {Both} and {Y} = {Only Y} + {Both}, then if you substitute you get:
 {Total} = {Only X} + {Only Y} + {Both} + {Neither}

You should apply the one which best suits the question at hand.

LinaNY · Answer

Thanks, Bunuel! it's clear now.

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A data company recently conducted a survey to determine wh

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