For Integers A and B, if SQRT(A^3 - A^2 -B) = 7, what is the : DS Archive
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# For Integers A and B, if SQRT(A^3 - A^2 -B) = 7, what is the

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For Integers A and B, if SQRT(A^3 - A^2 -B) = 7, what is the [#permalink]

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15 Nov 2004, 12:10
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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
Director
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15 Nov 2004, 12:28
I pick C as well.

S(1) gives a = 4 , -3 insufficient
S(2) gives b= 2, -1 insufficient

but using 1 & 2 we can solve for a.
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15 Nov 2004, 13:21
Im getting C..

Statement 1-

a^3-a^2-b=49
12a-b=49-------- insuff.

statement 2-

after all the simplification i get a^3-a^2-b^2=47 .... insuff.

combining both,

(b+1)(b-2)=0

b=-1 or 2
substituting for a in statement 1, a= 4 or 17/4. we can leave out the last value, since a= integer.
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Let's get it right!!!!

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15 Nov 2004, 13:27
I do not understand. Could some one explain this in itsy bitsy bits!

Ta very mcuh!
Director
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15 Nov 2004, 13:38
I would choose B.

Statement 1 is unuseful : A = 4 or -3

Statement 2 : B = 2 or -1

we know from the stem that sqrt(A^3-A^2-B)=7 => A^3-A^2=48 or 51
A being an integer only A=4 matches with 48
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15 Nov 2004, 13:47
twixt,
You got it

It's B.
I find it a very difficult question.
I wonder, How long did it take you to solve this one ?
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15 Nov 2004, 14:15
Keep posting this kind of hard DS Dookie this is good brainstorm material !

By the way where are they from ?

This one took me 12 lines on a scratch paper, 3 minutes I guess. I was suspicious as I had a really similar one during the real test and I always try to be cautious when dealing with integers and well rounded results
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15 Nov 2004, 18:11

thanks twixt for the solution and Dookie for posting this problem!
15 Nov 2004, 18:11
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