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# Which of the following must be non-negative?

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SVP
Joined: 06 Sep 2013
Posts: 1866
Concentration: Finance
Which of the following must be non-negative?  [#permalink]

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01 Feb 2014, 15:10
1
00:00

Difficulty:

55% (hard)

Question Stats:

59% (00:53) correct 41% (01:02) wrong based on 202 sessions

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Which of the following must be non-negative?

A. (a-0.9)(a-1)

B. (a+1)(a-1)

C. (a+0.9)(a+1)

D. (a-0.9)(a-0.9)

E. a(a+1)
Math Expert
Joined: 02 Sep 2009
Posts: 47168
Re: Which of the following must be non-negative?  [#permalink]

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02 Feb 2014, 02:24
4
2
jlgdr wrote:
Which of the following must be non-negative?

A. (a-0.9)(a-1)

B. (a+1)(a-1)

C. (a+0.9)(a+1)

D. (a-0.9)(a-0.9)

E. a(a+1)

5-sec approach:

D. (a-0.9)(a-0.9) = (a-0.9)^2. The square of a number is always non-negative.

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##### General Discussion
SVP
Joined: 06 Sep 2013
Posts: 1866
Concentration: Finance
Re: Which of the following must be non-negative?  [#permalink]

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01 Feb 2014, 15:11
+1 Kudos for anyone that comes with a good approach for solving this one

I thought that a^2 + a was always >=0 but apparently this is not the case so answer E is incorrect

Thanks
Cheers
J
Manager
Joined: 20 Dec 2013
Posts: 248
Location: India
Re: Which of the following must be non-negative?  [#permalink]

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01 Feb 2014, 21:01
1
I used a bit of calculus to do this.
Starting from E(because it 'seems' correct)
a^2+a
f'(a)=2a+1=0 => a=-1/2
f''(a) =2>0 => a= -1/2 is point of minima Putting this value in main equation we get -1/2 (-ve)

Option D
F(a)=(a - 0.9)^2
f'(a)= 2(a-0.9)=0 => a=0.9
f''(a)= 2>0 => a= 0.9 is point of minima. Putting in main equation we get 0 which is non negative.
Correct.

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Senior Manager
Joined: 06 Aug 2011
Posts: 360
Re: Which of the following must be non-negative?  [#permalink]

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01 Feb 2014, 23:05
1
jlgdr wrote:
Which of the following must be non-negative?

A. (a-0.9)(a-1)

B. (a+1)(a-1)

C. (a+0.9)(a+1)

D. (a-0.9)(a-0.9)

E. a(a+1)

I was jst doing Poe.
A) take a value positive and negative u l get the diff value..
b) same as A.. assume a negative u l get positive and negative ans both
C) same as A and B.
D) I stoped here.. tried both negative and positive value.. i was geting ans 0 or positive..didnt get any neggative value..
E) leave it.. it can b anything.
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Manager
Joined: 20 Dec 2013
Posts: 248
Location: India
Re: Which of the following must be non-negative?  [#permalink]

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02 Feb 2014, 02:49
Thats what over-excitement coupled with an opportunity to earn Kudos does;couldn't see the simple solution suggested by Bunuel!

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Senior Manager
Joined: 06 Aug 2011
Posts: 360
Re: Which of the following must be non-negative?  [#permalink]

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02 Feb 2014, 11:00
Wow Bunuel.. y this thing didnt cm in my mind !

+1
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Joined: 09 Sep 2013
Posts: 7326
Re: Which of the following must be non-negative?  [#permalink]

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16 Aug 2017, 07:36
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Which of the following must be non-negative? &nbs [#permalink] 16 Aug 2017, 07:36
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