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## Princeton Question

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f2001290 Master | Next Rank: 500 Posts
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#### Princeton Question

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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f2001290 Master | Next Rank: 500 Posts
Joined
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Posted:
400 messages
Followed by:
1 members
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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

jayhawk2001 Community Manager
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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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