If a - b ((b+c-a)^2)^(1/2) which of the following must be true?

Question

If a-b > \sqrt{(b+c-a)^2} which of the following must be true? A. a>0 B. a0 E. c<0

Gemelo90 · Answer

I was testing different numbers and came to the conclusion that B always has to be true.

adityagupta2102 · Answer

D.

a-b > sq. root

sq. root  = sq. root  =sq. root 
 Since, a-b > sq. root

a-b-c should be less than a-b 
So c must be positive.

Don't know whether it is right.

adityagupta2102 · Answer

a-b is always greater than 0. Since it involves a square root of a square which is always a positive or a zero.
So a-b > 0
a>b.

AkshdeepS · Answer

Given :  a-b > \sqrt{(b+c-a)^2}

We know that  \sqrt{(x)^2}  =  |x|

So,  a - b > |b+c-a|

Therefore we have 2 cases :

Case 1 :

a - b > b + c - a

2a - 2b > c

a - b > \frac{c}{2}  (No match)

Case 2:

a - b > -(b + c - a)

a - b > - b - c + a

a - a - b + b > - c

0 > - c

c > 0

(D)

GMATBusters · Answer

Another Approach:

GMATBusters · Answer

Another approach:
(a-b) > 0 because square root is always non negative.
therefore, (b-a) < 0
hence c must be >0, so that (b+c-a) is non negative. 
(If (b+c-a) is negative, square root is not defined)

Hence, c > 0

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.

If a - b > ((b+c-a)^2)^(1/2) which of the following must be true?

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