Princeton Question

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f2001290: Master | Next Rank: 500 Posts; Posts: 400; Joined: Sat Mar 10, 2007 4:04 amFollowed by: 1 member; Thanked: 1 times

by f2001290 » Sun May 06, 2007 1:05 am

For integers a and b, if sqrt(a^3 - a^2 - b) = 7, what is the value of a ?

1. a^2 - a = 12
2. b^2 - b = 2

Please explain the solution for this problem.

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Source: Beat The GMAT — Data Sufficiency | Sun May 06, 2007 1:05 am

jayhawk2001: Community Manager; Posts: 789; Joined: Sun Jan 28, 2007 3:51 pmFollowed by: 1 member; Location: Silicon valley, California; Thanked: 30 times

Re: Princeton Question

by jayhawk2001 » Sun May 06, 2007 11:16 am

f2001290 wrote:For integers a and b, if sqrt(a^3 - a^2 - b) = 7, what is the value of a ?

1. a^2 - a = 12
2. b^2 - b = 2

Please explain the solution for this problem.

Using (1), you get a^2 -a - 12 = 0 which implies a = 4 or a = -3.
Hence insufficient.

Using (2), b^2 -b -2 = 0 which implies b = 2 or b = -1

a^3 - a^2 - b = 49
a^2(a-1) = 49 + b

We know a(a-1) should be even. so, b = -1

So, a^2(a-1) = 48

Only a=4 satisfies above eqn. sufficient.

Hence B

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f2001290: Master | Next Rank: 500 Posts; Posts: 400; Joined: Sat Mar 10, 2007 4:04 amFollowed by: 1 member; Thanked: 1 times

by f2001290 » Sun May 06, 2007 8:02 pm

Jay Hawk

Did you score a 800 in GMAT?

You don't leave any questions in PS unanswered

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