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gmatprep 1 convention attendees

Expert replies
by vkb16 » Tue Feb 17, 2009 4:26 am
the attendees at a certain convention purchased a total of 15,000 books. How many of these attendees were female?

1. there was a total of 4000 attendees at the convention
2. the male attendees purchased an average (a. mean) of 3 books each, and the female attendees purchased an average of 5 books each.

i think E

ans is C

please help me understand the reason
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Source: — Data Sufficiency |

by DanaJ » Tue Feb 17, 2009 4:39 am
Say we use the following notations:
t = total number of books
m = male buyers
f = female buyers
ma = average number of books bought by male buyers
fa = average number of books bought by female buyers
You get that t = m*ma + f*fa = 15 000 and you are looking for f.
1. tells us that m + f = 4 000. However, we do not have any additional info regarding the relationship between m and f. This is why 1 is insufficient.
2. means that ma = 3 and fa = 5, making t = 3m + 5f = 15 000. This doesn't help establish f either, since you don't know any further info about f and m.

Now, but both equations together and you have a system of two unknowns and two equations, easily solvable:
m + f = 4 000
3m + 5f = 15 000.

So C is indeed correct.
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by vkb16 » Tue Feb 17, 2009 8:58 pm
thanks a lot!
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