In a town of 8,000 residents, 65 percent of all residents own a car

Question

In a town of 8,000 residents, 65 percent of all residents own a car, 55 percent own a motorcycle, and 25 percent own neither a car nor a motorcycle. How many residents own a car but not a motorcycle?

A. 800
B. 1,600
C. 2,000
D. 3,600
E. 4,400

BrentGMATPrepNow · Accepted Answer

Another approach is to use the  Double Matrix Method . 
This technique can be used for most questions featuring a population in which each member has two characteristics associated with it (aka overlapping sets questions). 
Here, we have a population of residents, and the two characteristics are: 
- own a car or do not own a car
- own a motorcycle or do not own a motorcycle

65% of 8000 = 5200
55% of 8000 = 4400
25% of 8000 = 2000

So, our matrix looks like this so far: 
 https://i.imgur.com/U3kEpMp.png

Since there are 8000 resident altogether, we know that, if 5200 own a car, then 2800 do NOT own a car
And, if 4400 own a motorcycle, then 3600 do NOT own a motorcycle
We get: 
 https://i.imgur.com/t0HfNT3.png

When we fill in the rest of the matrix we get: 
 https://i.imgur.com/X1qDNxS.png

We can see that   1600   residents own a car but not a motorcycle.

Answer: B

This question type is  VERY COMMON  on the GMAT, so be sure to master the technique.

To learn more about the Double Matrix Method, watch this video:
 https://www.youtube.com/watch?v=jK-tiBrrf04

Tan2017 · Answer

Let the total no of residents be 100

No of Residents who own a car=65
No of Residents who own a motorcycle=55
No of Residents who own neither=25

Therefore no of residents who own either car or motorcycle=100-25=75

No of residents who own both car and motorcycle= (55+65)-75=45

Hence no of residents who own only car=65-45=20

Now when the no of residents are 100, no of residents who own only car=20
When no of residents=8000, no of residents who own only car=20/100*8000=1600

IMO=B

HKD1710 · Answer

Total - neither = first + second - both

100 - 25 = 65 + 55 - Both

Both = 45

Only CAR = Car - Both = 65 - 45 = 20

But 20 is percent. hence 20% of 8000 = 1600.

Trick: An easy question sometimes comes with high penalty. After we are done with the question, always review what is asked. this question tries to trick on the same.

Bunuel · Answer

In a town of 8,000 residents, 65 percent of all residents own a car, 55 percent own a motorcycle, and 25 percent own neither a car nor a motorcycle. How many residents own a car but not a motorcycle?

A. 800

B. 1,600

C. 2,000

D. 3,600

E. 4,400

65 percent of all residents own a car: {Car} = 0.65*8,000 = 5,200;
55 percent own a motorcycle: {Motorcycle} = 0.55*8,000 = 4,400;
25 percent own neither a car nor a motorcycle: {Neither} = 0.25*8,000 = 2,000.

{Total} = {Car} + {Motorcycle} - {Both} + {Neither};
8,000 = 5,200 + 4,400 - {Both} + 2,000;
{Both} = 3,600.

The number of residents who own a car but not a motorcycle = {Car} - {Both} = 5,200 - 3,600 = 1,600.

Answer: B.

fskilnik · Answer

?\,\, = \,x = 65\% \left( {{\rm{Tot}}} \right) - {\rm{both}}

https://preview.ibb.co/e3ZYY0/17-Oct18-5r.gif

75\% \left( {{\rm{Tot}}} \right) = 65\% \left( {{\rm{Tot}}} \right) + 55\% \left( {{\rm{Tot}}} \right) - {\rm{both}}\,\,\,\,\,\,\left \,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{\rm{both}} = 45\% \left( {{\rm{Tot}}} \right)

? = 20\% \left( {{\rm{Tot}}} \right) = {1 \over 5}\left( {800 \cdot 10} \right) = 2 \cdot 800 = 1600

This solution follows the notations and rationale taught in the GMATH method.

Regards, 
Fabio.

ScottTargetTestPrep · Answer

Let’s start with making the total 100 percent; thus:

Total = Car owners + Motorcycle owners - both + neither

100 = 65 + 55 - both + 25

100 = 145 - both

Both = 45

So 65 - 45 = 20 percent of the 8,000 residents own a car but not a motorcycle, and 20% of 8,000 is 0.2 x 8,000 = 1,600.

Answer: B

bumpbot · Answer

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In a town of 8,000 residents, 65 percent of all residents own a car

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In a town of 8,000 residents, 65 percent of all residents own a car

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