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# Q is from one of the top three Test Prep company (I am not

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Manager
Joined: 25 Jul 2006
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Q is from one of the top three Test Prep company (I am not [#permalink]

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16 Feb 2007, 19:49
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

Q is from one of the top three Test Prep company (I am not naming them, bcoz I dont know what the laws are regarding posting their material on a forum)

Given
a^2 - 10a + 25 = b

The least possible value of b
1. 0
2. <0> 0
4. 1
5. Cannot be determined

I am confused with the answer they've given. Will post in next mesg.
Thanks!
Manager
Joined: 25 Jul 2006
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16 Feb 2007, 19:59
The answer they've given is 0.

Working backwards, it seems to me that it is bcoz in the general soln to the eqn (-b +- Root(b^2 - 4ac))/2a, the quantity under the Root sign will become negative if the RHS is less than 0.

This means that an Complex No. or (Real + Imaginary no. (Root of -ve no.)) is not a valid solution. But the question does not say only Real numbers are solutions. Is this an assumption in GMAT?

Secondly, is there another way to approach this problem besides checking for the value under the Root sign?

Thanks!
Senior Manager
Joined: 12 Mar 2006
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Schools: Kellogg School of Management
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16 Feb 2007, 21:49
The front instructions (which most of us dont really read) says that all numbers used are real numbers.

with regard to solving the problem, my approach would be the same

Discriminant should be greater than 0 so 'a' can be a real number

b^2 - 4*a*c >= 0

so 100 - 4*(25-b) >= 0

25 >= 25 - b

b >= 0
Manager
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16 Feb 2007, 23:09
Simplify to
(a-5)^2 = b.

b > 0 and it can be 0 when a = 5. Hence 0.
Manager
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17 Feb 2007, 16:30
prude, thanks much for your response to this as well as prior questions - my next question to is "how do you keep track of all these postings and respond with the correct answer ? - i barely get any time to study the material i have and by the time i finish one, i've forgotten the previous..."

question is rhetorical - dont mean to take any more of your time.
Manager
Joined: 25 Jul 2006
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17 Feb 2007, 16:35
jainvineet,

there is a typo in my posting - sorry - you may have been misled by it.
b>0 is one of the answer choices. it is not part of the question.
Intern
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17 Feb 2007, 17:10
oops wrote:
jainvineet,

there is a typo in my posting - sorry - you may have been misled by it.
b>0 is one of the answer choices. it is not part of the question.

Disable html when using '<' and '>'
17 Feb 2007, 17:10
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