Word Problems!

[Ahmed MS]

If everyone was charged the same fee, how many people came?

a. If the fee had been %0.75 less and 100 more people came the club would have received the same amount.
b. If fee had been $1.50 more and 100 fewer people came, the club would have received the same amount.

The answer is C, but according to me it should be E. Please help me out!

Cheers!

[Anurag@Gurome]

If everyone was charged the same fee, how many people came?

a. If the fee had been %0.75 less and 100 more people came the club would have received the same amount.
b. If fee had been $1.50 more and 100 fewer people came, the club would have received the same amount.

I think the % in statement 1 should be $.

Say, the fee was $P and n people came.

Statement 1: (n + 100)(P - 0.75) = nP
Hence, 100P - 0.75n - 75 = 0
We cannot find n as we have one equation but two unknown.

Not sufficient

Statement 1: (n - 100)(P + 1.5) = nP
Hence, 100P - 1.5n + 150 = 0
We cannot find n as we have one equation but two unknown.

Not sufficient

S1 & 2 Together: We can uniquely determine n as we have two equations in two unknown.

Sufficient

The correct answer is C.

[Ahmed MS]

Thanks Anurag! I am sorry about the error as I said I download from the web.

Cheers!