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Is the statement sufficient? - very basic Algebra question..

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by yumi2012 » Thu Aug 01, 2013 6:34 am
What are the roots of x²+kx-10

(1) one of the roots is -5

If one root is -5, we know one of the factors of the quadratic expression is (x+5). We now know the other factor is (x-2)...

--------------

Sorry I lack some basic knowledge of math.. How can one factor be (x+5)?
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by Brent@GMATPrepNow » Thu Aug 01, 2013 6:48 am
yumi2012 wrote:What are the roots of x²+kx-10

(1) one of the roots is -5

If one root is -5, we know one of the factors of the quadratic expression is (x+5). We now know the other factor is (x-2)...
It's important to recognize that your question is incomplete.
x² + kx - 10 cannot have any roots (solutions), because x² + kx - 10 is not an equation.
For example, we cannot ask someone to "solve" 2x + 5, but we can ask someone to solve 2x + 5 = 11

I'm going to assume that the original question says . . .
What are the roots of x² + kx - 10 = 0

(1) one of the roots is -5
Statement 1: one of the roots is -5

If one of the roots is -5, then x = -5 is a solution to the equation.
So, we can not plug x = -5 into the equation to get: (-5)² + k(-5) - 10 = 0
Simplify: 25 - 5k - 10 = 0
Simplify: 15 - 5k = 0
Solve: k = 3

So, the equation is x² + 3x - 10 = 0
Now that we know the equation, we can definitely find its roots (of course, we don't need to actually find the roots. We need only determine that we could find them)
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

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Brent
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by Brent@GMATPrepNow » Thu Aug 01, 2013 8:08 am
If you're interested, I created a similar (but SUPER HARD) question for BTG a few years ago: https://www.beatthegmat.com/mba/2010/09/ ... er-13-2010

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by Matt@VeritasPrep » Thu Aug 01, 2013 9:35 am
Brent@GMATPrepNow wrote:It's important to recognize that your question is incomplete.
x² + kx - 10 cannot have any roots (solutions), because x² + kx - 10 is not an equation.
For example, we cannot ask someone to "solve" 2x + 5, but we can ask someone to solve 2x + 5 = 11
I agree with you, Brent, but I'm not sure the GMAC (or some other question writers) do(es) - I've seen a lot of questions that assume that "the roots of ax² + bx + c" implies "the roots of ax² + bx + c = 0". (Otherwise why would you be asking for the roots? Even if the equation isn't = 0, you'd simply subtract the constant to make it so.)

The GMAT seems to make this assumption too, IIRC, but I don't know for sure: does anyone know if the GMAC has addressed this?
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by Brent@GMATPrepNow » Thu Aug 01, 2013 10:02 am
I'm not entirely sure I agree with you, Matt (although I could be wrong)

From the Official Guide:
The solutions of an equation are also called the roots of the equation. These roots can be checked by substituting them into the original equation to determine whether they satisfy the equation

Asking test-takers to find the root of an expression (like 3x) seems too ambiguous for the GMAT. Are there some specific (official) questions you're thinking of?

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