BTGmoderatorDC wrote:Each person attending a fund-raising party for a certain club was charged the same admission fee. How many people attended the party?
(1) If the admission fee had been 0.75$ less and 100 more people had attended, the club would have received the same amount in admission fee.
(2) If the admission fee had been 1.50$ more and 100 fewer people had attended, the club would have received the same amount in admission fee.
OA C
Source: GMAT Prep
The question is not transcripted correctly. In Statement 2, 'more' should be there for 'less.'
Say the admission fee is $x per person and n number of people attended the party.
Thus, total admission fee = $xn
We have to get the value of n.
Let's take each statement one by one.
(1) If the admission fee had been 0.75$ less and 100 more people had attended, the club would have received the same amount in admission fee.
=> xn = (x - 0.75)(n + 100)
xn = xn - 0.75n + 100x - 75
0.75n - 100x = -75 ---(1)
Can't get the unique value of n. Insufficient.
(2) If the admission fee had been 1.50$
more and 100 fewer people had attended, the club would have received the same amount in admission fee.
=> xn = (x + 1.50)(n - 100)
xn = xn + 1.5n - 100x - 150
1.5n - 100x = 150 ---(2)
Can't get the unique value of n. Insufficient.
(1) and (2) together
So, we have eqn (1) and eqn (2)
0.75n - 100x = -75 ---(1)
1.5n - 100x = 150 ---(2)
From (1) - (2), we get
-0.75n = -225
n = 300.
Sufficient.
The correct answer:
C
Hope this helps!
-Jay
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