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In a town of 8,000 residents, 65 percent of all residents own a car
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10 Apr 2017, 18:30

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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?

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11 Apr 2017, 10:19

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mkrishnabbdr wrote:

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

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.
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In a town of 8,000 residents, 65 percent of all residents own a car
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11 Apr 2017, 10:47

mkrishnabbdr wrote:

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

1. Make a venn diagram 2. Put 25% on the outside for neither 3. Start with 65% in the car circle, 25% in the motorcycle circle and 0% in the middle. 4. Keep putting more and more percent into the middle until the venn diagram equals 75% 5. For instance the original 65% + 55% = 120%. If you put 10% in the middle this becomes 55%+45%+10%=110%

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22 Apr 2017, 22:28

mkrishnabbdr wrote:

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

I solved this rather quickly if 65% + 55% = 120% then 20% of 8,000 = 1,600. It gives the correct answer, but was this complete luck?

Re: In a town of 8,000 residents, 65 percent of all residents own a car
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03 Jan 2018, 19:31

Total = Car+Motor-Both+None -> 100=65+55-Both+25 -> Both=45 The percentage of people owning cars only = 65-55=20 The number of people owning cars only = 20%*8000=1600 Answer: B

Re: In a town of 8,000 residents, 65 percent of all residents own a car
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03 Jan 2018, 19:55

Hi those having difficulty in this.. 65% - car 55% motorcycle None - 25%, so ATLEAST one is 100-25=75% But out of 75%, 55% have a motorcycle, so remaining 75-55=20% have a car but NOT motorcycle... Ans 20% of 8000=1600 B

Re: In a town of 8,000 residents, 65 percent of all residents own a car
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03 Jan 2018, 20:03

amitpandey25 wrote:

Bunuel, Need help with this one.

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.

Re: In a town of 8,000 residents, 65 percent of all residents own a car
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04 Jan 2018, 05:57

Total (100%) = % Car + % motorcycle - %both +% neither => % both = Car + motorcycle + neither - total = 65% + 55% + 25% - 100% = 45% => % of people who own a car but not a motorcycle = % car - % both = 65% - 45% = 20% => The number of residents own a car but not a motorcycle = 8000*20% = 1600. Hence the answer is B.

Re: In a town of 8,000 residents, 65 percent of all residents own a car
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17 Jul 2018, 09:48

mkrishnabbdr wrote:

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

Total # of residents = 8000

% of residents that own a car = 65%

% of residents that own a motorcycle = 55%

% of residents that own none = 25%

Let X be the % of people that do not own a motorcycle.

Hence we have X = 100 - 55 = 45%

Now, % of people that do not own a motorcycle but own a car = 45 - 25 = 20%

# of residents that own a car but no motorcycle = 20% * 8000 = 1600

In a town of 8,000 residents, 65 percent of all residents own a car
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17 Oct 2018, 05:40

mkrishnabbdr wrote:

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?

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

Regards, Fabio.
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Re: In a town of 8,000 residents, 65 percent of all residents own a car
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17 Oct 2018, 06:57

Top Contributor

mkrishnabbdr wrote:

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

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:

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:

When we fill in the rest of the matrix we get:

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:

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Re: In a town of 8,000 residents, 65 percent of all residents own a car &nbs
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17 Oct 2018, 06:57