BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

If \(a-b > \sqrt{(b+c-a)^2}\) which of the following must be true?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Legendary Member
Posts: 2898
Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members
Thanked: 6 times
by Vincen » Wed Nov 17, 2021 7:36 am

Timer

00:00

Answers

A

B

C

D

E

Stats

Difficulty—

If \(a-b > \sqrt{(b+c-a)^2}\) which of the following must be true?

A. \(a>0\)

B. \(a<b\)

C. \(b=0\)

D. \(c>0\)

E. \(c<0\)

Answer: D

Source: Economist
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

Re: If \(a-b > \sqrt{(b+c-a)^2}\) which of the following must be true?

by regor60 » Wed Nov 17, 2021 10:45 am
Recognize that the right side is positive, so A must be greater than B.

Unfortunately, that is not one of the answer choices. Too bad.

For a given result on the right side, there are two ways to achieve this.

If B+C>A, then right side equals B+C-A.

For example, B=2, C=4 and A=5. So right side would equal 1.

So, A-B >B+C-A. Unfortunately, this doesn't help us since any manipulation of this won't yield any of the answer choices. Too bad again.

However, right side can also = 1 if B+C-A= -1, since squaring -1=1 and square root of 1=1.
B could=2, C=4 and A=7 for example.
But squaring this and taking the square root loses the relationship between A,B and C.

Fortunately B+C-A can be rewritten as A-B-C to yield +1 in this example.

So, in this situation, A-B>A-B-C

Subtract A and add B to both sides yields 0>-C. This is only true if
C>0 D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 416
Joined: Thu Oct 15, 2009 11:52 am
Thanked: 27 times

Re: If \(a-b > \sqrt{(b+c-a)^2}\) which of the following must be true?

by regor60 » Wed Nov 17, 2021 1:00 pm
Another way, probably better.

Rearrange B+C-A to be C-(A-B)

Call (A-B)= X

Now X > $$\sqrt{\left(C-X\right)}^2$$

Square both sides

X $$^2$$ > $$^{\left(C-X\right)^2}$$

So $$^{\left(X^2\right)}$$ > $$^{\left(C^2\right)}$$ -2XC+ $$^{\left(X^2\right)}$$

Subtract $$^{\left(X^2\right)}$$ from both sides

0>C(C-2X)

This can only be true if either
C>0 and (C-2X)<0
Or
C<0 and (C-2X)>0

Let's examine the second choice first

For C-2X >0 C must be> 2X

2X=2(A-B) from our substitution.

But A is greater than B because the right side of the problem statement is positive always, so 2(A-B) is positive.

But for C to be greater than 2(A-B) means therefore that C>0.

But C can't be >0 per the condition, creating a contradiction, so the second choice is eliminated, leaving only the first choice C>0 D
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1