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 →

(x - 1)^2 = 400 -> ?? Positive square root quesiton

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Senior | Next Rank: 100 Posts
Posts: 38
Joined: Sat Nov 21, 2009 1:56 pm
Location: Indianapolis
Thanked: 2 times
GMAT Score:760
by MFaulkner » Wed May 05, 2010 2:55 pm
If (x - 1)^2 = 400, which of the following could be the value of x-5?

A. 15
B. 14
C. -24
D. -25
E. -26

The answer is C, -24.

I can do this simply by taking the square root of each side and obtaining:

x - 1 = +/- 20
x - 1 = 20 OR x - 1 = -20
Therefore, x=21, or x=-19

Then, (-19 - 5) = choice C, -24

However, I was under the impression that positive or even square roots on the GMAT are ALWAYS positive. So I got this one wrong b/c I took the square root of each side and obtained only one solution: (x - 1) = +20, therefore x = 21

Can someone explain to me why this OG problem is using +/- for an positive & even square root??

Thank you!
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 1179
Joined: Sun Apr 11, 2010 9:07 pmFollowed by: 88 members
Location: Milpitas, CA
Thanked: 447 times

by Rahul@gurome » Wed May 05, 2010 6:58 pm
Solution
If the question had been (x-1) = (400)^(1/2) then we would have taken just the positive square root of 400 that is 20 but since the question is (x-1)^2 = 400, we have to take both positive and negative roots.
Rahul Lakhani
Quant Expert
Gurome, Inc.
https://www.GuroMe.com
On MBA sabbatical (at ISB) for 2011-12 - will stay active as time permits
1-800-566-4043 (USA)
+91-99201 32411 (India)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Sat Jul 14, 2018 6:36 pm
MFaulkner wrote:If (x - 1)^2 = 400, which of the following could be the value of x-5?

A. 15
B. 14
C. -24
D. -25
E. -26
Taking the square root of both sides, we have:

(x - 1)^2 = 400

√(x - 1)^2 = √400

This gives us:

|x - 1| = 20

This absolute value equation requires that we use two cases to determine all possible values of x.

Case 1. When (x-1) is positive:

x - 1 = 20

x = 21

Case 2. When (x-1) is negative:

-(x - 1) = 20

-x + 1 = 20

-x =19

x = -19

Thus, (x - 5) can equal either 21 - 5 = 16 or -19 - 5 = -24.

Answer: C

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
Elite Legendary Member
Posts: 10392
Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members
Location: Palo Alto, CA
Thanked: 2867 times
GMAT Score:800

by [email protected] » Mon Jul 16, 2018 9:20 pm
Hi All,

GMAT writers often provide little 'hints' in the wording of the question that can help you to avoid some of the work. Here, notice the phrase "...which of the following COULD be the value...." That's an interesting way to phrase a question - it's NOT asking "...what IS the value...." - it's asking "what COULD be the value...."

This implies that there's MORE than 1 answer AND that the 'obvious' answer is not the one that's going to be listed.

With (X-1)^2 = 400....

I know there are two solutions (because of the 'squared sign')...

(X-1) COULD = 20 or -20

From the wording of the prompt though, it's likely that the "-20 option" is the one that we supposed to be going after, since that's the less obvious solution.

X-1 = -20
X = -19

We're asked for a possible value of X-5, so in this case (X-5) = -24.

Obviously, there's nothing wrong with being thorough and finding BOTH answers, but the question didn't ASK for that, so you have to be mindful about how much extra work you might be doing (and how much extra time you might be spending) on a given question, especially if you have a pacing problem.

Final Answer: C

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 2095
Joined: Tue Dec 04, 2012 3:22 pmFollowed by: 247 members
Thanked: 1443 times

by ceilidh.erickson » Thu Jul 19, 2018 5:19 am
MFaulkner wrote: However, I was under the impression that positive or even square roots on the GMAT are ALWAYS positive. So I got this one wrong b/c I took the square root of each side and obtained only one solution: (x - 1) = +20, therefore x = 21

Can someone explain to me why this OG problem is using +/- for an positive & even square root??
To answer your actual question here:

When the GMAT given you a root *symbol*, as in √16, this represents just a positive number. This is understood to only have one value so that a question such as the following can have a single answer: https://www.beatthegmat.com/sqrt-80-t290557.html

If you're given that x^2 = 16, then you perform the operation of square rooting both sides; this is when you get a positive & negative solution.
Ceilidh Erickson
EdM in Mind, Brain, and Education
Harvard Graduate School of Education
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1