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Which of the following must be non-negative?

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Bunuel
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Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   01 May 2021, 07:30
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A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

56% (01:33) correct 44% (01:25) wrong based on 71 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)
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D
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Showmeyaa
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Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   Updated on: 01 May 2021, 08:19
Bunuel 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)



Option D.
\((a-0.9)(a-0.9) = (a-0.9)^2\)
Square of a number is always non-negative(PS: It can also be 0 as 0 is non-negative)
Edit: Corrected my reasoning of assuming 'a' to be an integer.

Originally posted by Showmeyaa on 01 May 2021, 07:38.
Last edited by Showmeyaa on 01 May 2021, 08:19, edited 1 time in total.
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chetan2u
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Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   01 May 2021, 07:46
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Showmeyaa wrote:
Bunuel 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)



Option E.
Reasoning: The product of two consecutive integers will always be non-negative.
PS: It can be zero and zero is a non-negative number.


Be careful with variables.
It is nowhere written that a is an integer.
So, a(a+1) will be negative when a is between 0 and -1. For example a=-0.5, so -0.5*0.5=-0.25

Answer is (a-0.9)(a-0.9)

\((a-0.9)(a-0.9)=(a-0.9)^2\)
Squares are always non negative

D
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Re: Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   01 May 2021, 07:55
chetan2u wrote:
Showmeyaa wrote:
Bunuel 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)



Option E.
Reasoning: The product of two consecutive integers will always be non-negative.
PS: It can be zero and zero is a non-negative number.


Be careful with variables.
It is nowhere written that a is an integer.
So, a(a+1) will be negative when a is between 0 and -1. For example a=-0.5, so -0.5*0.5=-0.25

Answer is (a-0.9)(a-0.9)

\((a-0.9)(a-0.9)=(a-0.9)^2\)
Squares are always non negative

D


Thanks a lot chetan2u, got my mistake. Not sure, why I took it to be an integer.
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Re: Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   01 May 2021, 07:56
Bunuel 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)


Option D

D) ... can be simplified to \((a-0.9)^2\) . Square of any number is \(>= 0\), in other words its always non negative.

Since we are not sure whether "a" is positive or negative, we can not comment on other options.
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Re: Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   09 May 2021, 01:45
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Bunuel 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.

Answer: D.
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Re: Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   09 May 2021, 02:48
Quick question: Option B says (a+1)(a-1) = a^2 - 1^2. Can we prove that it can produce a negative number?
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Re: Which of the following must be non-negative? [#permalink] Which of the following must be non-negative?   09 May 2021, 03:02
D

It can be helpful to think of the rules regarding stuff like a^2 etc.

If you re-arrange (D), it's actually something similar to (a-b)^2 ... which is basically (d)^2 ... which has to be 0 or above.
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Re: Which of the following must be non-negative? [#permalink]
09 May 2021, 03:02
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