Each person attending a fund-raising party for a certain

[Guest]

The Answer is C.

Can someone please walk me through the algebra and/or logic underlying this problem?

Thanks!

The file is attached. This is from GMAT PrepTest (TM).

[a7lee]

n - Number of people
p - price of admission.

For part A) you can create the equation

n(p) = (p - 0.75)(n + 100)
np = np + 100p - .75n - 75.
100p - .75n = 75.

You only have one equation and two variables so you cannot solve for n.

For part B) you can create the equation.

n(p) = (p + 1.5)(n-100)
np = np -100p + 1.5n - 150
1.5n - 100p = 150.

Again B is insufficient because two variables and one equation.

Combine A+B, you immediately see that the two equations are distinct to each other. 2 equations 2 variables you know you can solve for n. So C is the answer.

[Guest]

a7lee -

Thank you for the algebraic explanation - makes sense now!

Can you/anyone else provide a logic-based explanation foir this problem as well? Is there one?

Thank you!