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In a town of 8,000 residents, 65 percent of all residents own a car [#permalink]
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10 Apr 2017, 19:30
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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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10 Apr 2017, 19:49
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=10025=75
No of residents who own both car and motorcycle= (55+65)75=45
Hence no of residents who own only car=6545=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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11 Apr 2017, 11:19
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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11 Apr 2017, 11:47
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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22 Apr 2017, 23:28
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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03 Jan 2018, 11:07
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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03 Jan 2018, 12:09
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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03 Jan 2018, 20:31
Total = Car+MotorBoth+None > 100=65+55Both+25 > Both=45 The percentage of people owning cars only = 6555=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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03 Jan 2018, 20:55
Hi those having difficulty in this.. 65%  car 55% motorcycle None  25%, so ATLEAST one is 10025=75% But out of 75%, 55% have a motorcycle, so remaining 7555=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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03 Jan 2018, 21:03
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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04 Jan 2018, 06:57
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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17 Jul 2018, 10:48
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. Thanks, GyM



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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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17 Jul 2018, 12:01
(80*65)+(80*55)+(80*25)2x=8000 ; 2x=common between car and motorcycle owner % 5200+4400+20008000=2x 3600=2x car=52003600=1600 Ans: B




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