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Each person attending a fund-raising party for a certain clu

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Each person attending a fund-raising party for a certain clu

by BTGmoderatorDC » Mon Dec 10, 2018 7:02 pm
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$ less and 100 fewer people had attended, the club would have received the same amount in admission fee

OA C

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by Jay@ManhattanReview » Tue Dec 11, 2018 4:04 am
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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by Mo2men » Wed Oct 09, 2019 2:20 pm
Jay@ManhattanReview wrote:
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
Hi Jay,

In statement 1, do we have many values that satisfy the statement 1 ? or only one set ? I feel that it is diophantine equation.

Thanks in advance
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