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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  [#permalink]

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New post 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?

A. 800

B. 1,600

C. 2,000

D. 3,600

E. 4,400
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 10 Apr 2017, 18:49
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
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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  [#permalink]

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New post 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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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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?
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 03 Jan 2018, 10:07
Bunuel,
Need help with this one.
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 03 Jan 2018, 11:09
Car = 65%
Motor = 55%
Both Car and Motor = x%

Neither Car or Motor = 25%
Car = A+x
Motor = B + x

A+ B- x = 75
x=45%

A+ x = 65%
A = 20%

20% of 8000 = 1600
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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

Hope it helps
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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.

{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.
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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.
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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


Answer B.


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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 17 Jul 2018, 11:01
(80*65)+(80*55)+(80*25)-2x=8000 ; 2x=common between car and motorcycle owner %
5200+4400+2000-8000=2x
3600=2x
car=5200-3600=1600
Ans: B
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In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 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?

A. 800

B. 1,600

C. 2,000

D. 3,600

E. 4,400

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

Image


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

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


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

Regards,
Fabio.
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Re: In a town of 8,000 residents, 65 percent of all residents own a car  [#permalink]

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New post 17 Oct 2018, 06:57
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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


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:
Image

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:
Image

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

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 [#permalink] 17 Oct 2018, 06:57
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