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Joined: 08 Nov 2009
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WE 1: Supply Chain Management
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Number properties I question #2 [#permalink]
 27 Nov 2009, 14:43
I tried looking for an explanation for this before posting but hand no luck. If some one could point me to a thread that would be great!
Is A positive?
1. x^2 - 2x + A is positive for all x
2. Ax^2 + 1 is positive for all x
My question is is on statement 1, if x=-1 wouldnt it be possible for A to be negative? -1^2 + -2*(-1) + A = 1+2+A =3+A. Therfore A could be -2 and the statement would still be positive.
What am i missing here?
Thanks,
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Tuck Thread Master
Joined: 20 Aug 2009
Posts: 314
Location: Tbilisi, Georgia
Schools: Stanford (in), Tuck (WL), Wharton (ding), Cornell (in)
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Re: Number properties I question #2 [#permalink]
28 Nov 2009, 02:45
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1. x^2 - 2x + A is positive for all x
When x=0, x^2 - 2x + A=A. According to Statement1 it should be positive, soA>0, SUFF
2.Ax^2 + 1 is positive for all x
Ax^2 + 1>0
Ax^2>-1
Here x^2 is always positive, but A could be both positive OR negative. Consider x=1/3, A=-1; Ax^2=-1/9>-1
INSUFF
Answer: (A)
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Intern
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Re: Number properties I question #2 [#permalink]
28 Nov 2009, 07:53
Thanks for the clarification.
That helped me realize how i was thinking of A as a variable and not a constant.
Thanks,
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Re: Number properties I question #2
[#permalink]
28 Nov 2009, 07:53
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