In a town of 8,000 residents

[ashwinrkamath]

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?
800
1,600
2,000
3,600
4,400

now in this question, in the explanation we have calculated the number of peole not having motorcycle from 8000, i.e. 8000 - 4400 = 3600, out of which we subtract the ones that don't have either making it
3600 - 2000 = 1600
But is it necessary that all these 1600 people will own a car?
because:
out of 8000 - 2000 = 6000 people own a car or motorcycle or both.

5200 - car
4400 - motorcycle

which doens't mean 6000 - 4400 = 1600 people own a car but not a motorcycle. What about the 800 people that don't own a car?

Am i going wrong somewhere. Please explain!!!
Thanks

[adiagr]

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?
800
1,600
2,000
3,600
4,400

now in this question, in the explanation we have calculated the number of peole not having motorcycle from 8000, i.e. 8000 - 4400 = 3600, out of which we subtract the ones that don't have either making it
3600 - 2000 = 1600
But is it necessary that all these 1600 people will own a car?
because:
out of 8000 - 2000 = 6000 people own a car or motorcycle or both.

5200 - car
4400 - motorcycle

which doens't mean 6000 - 4400 = 1600 people own a car but not a motorcycle. What about the 800 people that don't own a car?

Am i going wrong somewhere. Please explain!!!
Thanks

A table is the best way to avoid all confusions.

--------Car------No Car----
|
MC-----XXX-------YYY------4400
|
No MC----A------2000-------B
---------5200---------------8000


XXX and YYY are unknown values


B = 8000 - 4400 = 3600

A= 3600 - 2000 = 1600

Our desired answer is A.

[mschwrtz]

adiagr's answer is perfectly correct. It's much more important, ashwinrkamath, that you develop such a method to avoid errors than it is that you understand exactly what error you made.

Still, it must be frustrating to not see how your math could be wrong, so let's expand a bit.

-I think that you, ashwinrkamath, lost track of what those numbers represented. 6000 is the number who own just a car, just a motorcycle, or both a car and a motorcycle (6000=c+m+b). 5200 is the number who own a just a car, or both a car and a motorcycle (5200=c+b). That leaves 800 who own just a motorcycle (800=m).
-The double-set matrix to which adiagr refers is the ideal default tool for overlapping-set questions, questions in which one group (e.g. the town's residents) are divided according to two distinct yes-no criteria (e.g. owning or not owning a car, owning or not owning a motorcycle).
-Only a few questions about such overlapping sets can be readily answered without appeal to a DSM.
-This might be one of them, but there's no real reason to pursue that if you don't see it right away. Just use the DSM.
-This question relies on a property of overlapping sets, that the union of two sets (e.g. the number who own just a car, just a motorcycle, or both a car and a motorcycle) is equal to the the sum of the two sets (e.g. car owners PLUS the motorcycle owners) minus the overlap (e.g. the number who own both a car and a motorcycle).
-In this case, and in percent terms, that means that 75%=(65%+55%)-45%. If 55% own a motorcycle, and 45% own both a car and a motorcycle, then 10% own just a motorcycle.

[ashwinrkamath]

Thanks!!!!

Although i understand that using tables for such questions makes it easier, i personally don't like to use them.

I'll try and get a hang of them before i write GMAT.

Anyways, thanks for the replies. I got to know where i was going wrong. I think it was more because of burning out that day because the question seems so easy today.

Here is my approach:
No of people having cars = 5200
No of people having bikes = 4400
No of people who don't have either = 2000

Therefore, people with cars + people with bikes - people having both(coz it overlaps twice) = 6000

5200 + 4400 - x = 6000
x = 3600 ==> this is the number that overlaps.

people with only cars = 5200 - overlap No
= 5200 - 3600 = 1600


Thanks

[tim]

i agree with Michael. i can't stress enough the importance of using charts and tables for word translations problems. You may think you don't need them for the problems you've seen so far, but you may encounter problems on the GMAT that are sufficiently difficult your normal methods don't work. When this happens, you'll wish you had spent some time practicing the alternate approach.. :)

In general, i like to recommend that students try each math problem as many different ways as they can. Remember, your goal is not to get practice problems CORRECT, but rather to use them to develop skills you may need on the GMAT..

[debmalya.dutta]

Here is how I solved it ..
Using VENN diagram
Number of people who don't have either = 25%
So number of people who have one of them or both of them = 75% of population
So p(A U B) = p(A) + p(B) - p(A intersection B)
75 = 65 + 55 - X
X = 45
So % of people having only car = 65-45 = 20%
Hence number = 20% of 8000 = 1600

[mschwrtz]

I want to stress again that Venn diagrams are not generally a good tool for overlapping set questions.

You pretty much have to use them when you have three overlapping sets (a triple-set matrix would have three dimensions).

And even when you have only two overlapping sets Venn diagrams can easily track one particular property of overlapping sets (the one I mentioned above, that the union of two sets is equal to the the sum of the two sets minus the overlap).

Otherwise they're a great way to display info, but a poor way to manage it. I'll second Tim's idea of solving a question a number of different ways, though. What you'll generally discover solving overlapping-set questions with Venn diagrams is that it's really, really hard.