Which of the following must be non-negative?

Question

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)

Showmeyaa · Answer

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.

chetan2u · Answer

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

Showmeyaa · Answer

Thanks a lot  chetan2u , got my mistake. Not sure, why I took it to be an integer.

Shrey08 · Answer

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.

Bunuel · Answer

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.

ASR2021 · Answer

Quick question: Option B says (a+1)(a-1) = a^2 - 1^2. Can we prove that it can produce a negative number?

GmatKnightTutor · Answer

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.

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem Series ↧↧↧

https://www.youtube.com/watch?v=n-RW1wUURiw

We need to find which of the following must be non-negative?

A. (a-0.9)(a-1) :  will be negative for values of a between 0.9 and 1 as first term will be positive and second term will be negative  =>  FALSE

B. (a+1)(a-1) = a^2 - 1 :  will be negative for values of a between -1 and 1  =>  FALSE  
 
 C. (a+0.9)(a+1)   :  will be negative for values of a between -0.9 and -1 as first term will be negative and second term will be positive  =>    FALSE

D. (a-0.9)(a-0.9) = (a - 0.9)^2 :  since this is a square of a number so it will ALWAYS be non-negative  =>  TRUE

E. a(a+1) :   will be negative for values of a between -1 and 0 as a will be negative but (a+1) will be positive  =>  FALSE  
 
So,  Answer will be D 
Hope it helps!

Watch the following video to MASTER Inequalities

https://www.youtube.com/watch?v=1THrnWJtOqc

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

Which of the following must be non-negative?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

Which of the following must be non-negative?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards