GMAT Prep Questions

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okigbo: Master | Next Rank: 500 Posts; Posts: 177; Joined: Sun Aug 02, 2009 9:39 pm; Thanked: 6 times

by okigbo » Fri Sep 18, 2009 7:01 pm

Each person attending a fundraising 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 fees
2. If the admission fee had been $1.50 and 100 fewer people had attended, the club would have received the same amount in admission fees

In the xy-plane, at what two points does the graph of y=(x+a)(x-b) intersect the x-axis?
1. a+b=-1
2. The graph intersects the y-axis at (0,-6)

Thanks

Source: Beat The GMAT — Data Sufficiency | Fri Sep 18, 2009 7:01 pm

nand358: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sat Aug 15, 2009 10:36 pm; Location: San Diego CA

Re: GMAT Prep Questions

by nand358 » Mon Sep 21, 2009 9:09 pm

Question 1:
I believe there is a typo in the question. Stmt 2 should be $1.50 more. Now, moving onto the solution:

Lets say,
p = number of people who attended
a = admission fee per person in dollars

stmt 1: (a - 0.75)(p + 100) = pa ==> So, Insufficient to obtain p.
stmt 2: (a + 1.50)(p - 100) = pa ==> So, Insufficient to obtain p.

Stmt 1. and 2. together: SUFFICIENT to solve for p. It works out to 300 people.

Question 2:
Since, the question is relating to determining the point of intersection with the x-axis: y = 0.

So, (x + a)(x - b) = 0. This equation has two roots: x = -a and x = b.

stmt 1: a + b = -1 ==> Insufficient to determine a, b
stmt 2: substituting (0,-6) in the equation yields :

ab = 6. Insufficient to determine a, b.

But combining both a + b = -1 and ab = 6, we can get the values for a and b. So, stmt 1. and stmt 2. both put together can be solved for the points of intersection.

But the quadratic equations has no real roots.

Therefore, the function y = (x + a)(x - b) does not intersect the x axis.

Cheers,

Nand

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