Of the 500 business people surveyed, 78 percent said that they use the

Question

Of the 500 business people surveyed, 78 percent said that they use their laptop computers at home, 65 percent said that they use them in hotels, and 52 percent said that they use them both at home and in hotels. How many of the business people surveyed said that they do not use their laptop computers either at home or in hotels?

A. 45
B. 55
C. 65
D. 95
E. 130

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Can somebody give the formula for this overlapping set problem?
P(AUB) = P(A)+P(B)-P(A intersection B)
I tried to use the domain matrix learnt from MGMAT. But somewhere I am going wrong, can someone help?

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Official Answer

A

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aemarroquin · Accepted Answer

I kept everything in percentage form since that is how the information was presented. I did not want to introduce calculations that could lead to an error.

I used the group formula:

Total = Group 1 + Group 2 - Both + Neither.
 
Using the formula above and the information we are given:

100% = 78% + 65% - 52% + Neither

100% = 91% + Neither or

Neither = 100% - 91% = 9%

The total here is 500 so we can multiply 9% with 500 to get the amount of business people who do no use their laptops at home or in hotels.

(9/100) * 500 = 45
 
All of the methods mentioned above work, but I hope someone finds this helpful too. We can never have too many ways to approach a problem.

MacFauz · Answer

I guess you made a mathematical error. Personally, I prefer creating the matrix in percentages when the question is given in percentages. And finally multiply what I want with the total. However for illustration the matrix should be

moneymango · Answer

No reason to use formulas or weird pictures for this problem. Just think about what each set is.

I took the totals:
390 people use their laptop at home  
325 people use their laptop in hotels  
260 people use their laptop both in hotels and at home

Clearly if someone uses their laptop both in hotels and at home, they belong in both the previous two sets (1,2). By subtracting set 3 from the first two, we can determine the number of people that lie in set 1 or set 2 but not in set 3.

Gives us: 
130 only use their laptop at home
65 only use their laptop in hotels
260 use their laptop in both

add them up, subtract from the total and you get 45.

PareshGmat · Answer

Refer Venn diagram below:

DJ1986 · Answer

I used a chart like other people but left everything in percents and then calculated 9% of 500 = 45. I've found that the GMAT rewards you for procrastinating on doing calculations.

dimson · Answer

Instead of using 500, just use 100 and then multiply the final answer by 5.

T=G1+G2-Both+Neither
100=78+65-52+X
x=9
5*9=45

Takes 30 seconds.

MathRevolution · Answer

Home + Hotels - Both = 78 + 65 - 52 = 91%

Therefore, 100% - 91% = 9% neither use it

=>  \frac{9}{100}* 500 = 45

Answer A

DanTheGMATMan · Answer

Straightforward overlapping sets, don't convert until the end:

https://www.youtube.com/watch?v=s9DeNQthK1w

ShreyaMittal1609 · Answer

Hi Bunuel , in this question we have taken do NOT use their laptop computers either at home or in hotels?- means do not use both at home and hotels. Hence we are asked only other who use Neither. However in the below question- https://gmatclub.com/forum/how-many-int ... 26153.html Either 11 or 35 then- so here we counted all the numbers that are divisible by either 35 or 11 or both (AUB) I'm confused why usage of word Either is different in both the questions.

Bunuel · Answer

It is actually being used the  same way  in both.

“Either A or B” means  A or B or both .

So:
 
 “do  not  use laptops either at home or in hotels” = NOT(home OR hotels) =  neither  
 “not divisible by either 11 or 35” = NOT(divisible by 11 OR 35) =  divisible by neither

In the second question, we first count numbers divisible by 11 or 35 or both, and then subtract them from the total to get those divisible by neither.

Of the 500 business people surveyed, 78 percent said that they use the

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