December 09, 2018 December 09, 2018 07:00 AM PST 09:00 AM PST Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT. December 10, 2018 December 10, 2018 10:00 PM PST 11:00 PM PST Practice the one most important Quant section  Integer properties, and rapidly improve your skills.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 177

If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
20 Dec 2012, 08:07
Question Stats:
76% (01:14) correct 24% (01:36) wrong based on 899 sessions
HideShow timer Statistics
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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 51035

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
20 Dec 2012, 08:09



Intern
Joined: 21 Jan 2014
Posts: 11
Location: Germany
Concentration: Entrepreneurship, Strategy
GMAT Date: 05282014
GPA: 3.9
WE: Consulting (Entertainment and Sports)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
13 May 2014, 09:36
Hi, this is an interesting problem regarding the GMAT Club Math Book. I studied it and on page 15 it says: When the GMAT provides the square root sign for an even root, the only accepted answer is the positive root. That is, NOT +5 or 5. In contrast, the equation x^2 has TWO solutions, +5 and 5. Even roots have only a positive value on the GMAT. Due to this fact (which of course does not include this particular situation, because it's talking about the "sign"), I didn’t consider the negative root. Maybe a phrase, which could be improved on the next issue .



Manager
Joined: 12 Feb 2011
Posts: 87

If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
30 Jul 2014, 08:33
holdem wrote: Hi, this is an interesting problem regarding the GMAT Club Math Book. I studied it and on page 15 it says: When the GMAT provides the square root sign for an even root, the only accepted answer is the positive root. That is, NOT +5 or 5. In contrast, the equation x^2 has TWO solutions, +5 and 5. Even roots have only a positive value on the GMAT. Due to this fact (which of course does not include this particular situation, because it's talking about the "sign"), I didn’t consider the negative root. Maybe a phrase, which could be improved on the next issue . That statement from the book still holds good, it says "when GMAT provides the square root sign" whereas in this problem you were explicitly calculating the square root of 400 rather than GMAT providing \(\sqrt{400}\). Hope that helps.



Intern
Joined: 29 Oct 2014
Posts: 24

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Dec 2014, 22:04
Bunuel wrote: Walkabout 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 \((x  1)^2 = 400\) > \(x1=20\) or \(x1=20\) > \(x5=204=16\) or \(x5=204=24\). Answer: C. Hi there, where did the 4 come from? i.e. \(x5=20 4=16\) or \(x5=20 4=24\) Thanks.



Senior Manager
Joined: 13 Jun 2013
Posts: 276

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
09 Dec 2014, 01:15
ColdSushi wrote: Bunuel wrote: Walkabout 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 \((x  1)^2 = 400\) > \(x1=20\) or \(x1=20\) > \(x5=204=16\) or \(x5=204=24\). Answer: C. Hi there, where did the 4 come from? i.e. \(x5=20 4=16\) or \(x5=20 4=24\) Thanks. hi, remember we have calculated the value of x1=20 or 20. 1) x5 = (x1)4 now from 1, put the value of x1 as 20 or 20 = 204 =16 or x5 = (x1)4 = 204 = 24 i hope it helps.



Intern
Joined: 29 Oct 2014
Posts: 24

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
09 Dec 2014, 03:24
Hi there, where did the 4 come from? i.e. \(x5=204=16\) or \(x5=204=24\)
Thanks.[/quote]
hi, remember we have calculated the value of x1=20 or 20. 1) x5 = (x1)4 now from 1, put the value of x1 as 20 or 20 = 204 =16 or x5 = (x1)4 = 204 = 24
i hope it helps.[/quote]
Yep great  understand now. Appreciate your help!



Senior Manager
Status: Math is psychological
Joined: 07 Apr 2014
Posts: 420
Location: Netherlands
GMAT Date: 02112015
WE: Psychology and Counseling (Other)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
06 Jan 2015, 07:58
Could we also solve this like this:
(x1)^2 = (x1)(x1)?
I tried like this at first, but didn't end up well.. Unless I miscalculated sth somewhere.
Thank you.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13047
Location: United States (CA)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
06 Jan 2015, 10:17
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 (X1)^2 = 400 I know there are two solutions (because of the 'squared sign')... (X1) 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. 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. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13047
Location: United States (CA)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
06 Jan 2015, 10:28
Hi pacifist85, While you could convert the equation into a Quadratic, I don't think that you'll find that method to be particularly fast nor easy.... (X1)^2 = 400 (X1)(X1) = 400 X^2  2X + 1 = 400 X^2  2X  399 = 0 (X  21)(X + 19) = 0 X = 21 or 19 Now, contrast the above with the following.... (something)^2 = 400 (something) = +20 or 20 (X  1) = 20 or (X  1) = 20 X = 21 or 19 GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1826
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Jan 2015, 01:41
\((x  1)^2 = 400\) \(x  1 = \pm 20\) \(x = 1 \pm 20 = 21 OR 19\) x  5 = 215 = 16 OR 195 = 24 Answer = C
_________________
Kindly press "+1 Kudos" to appreciate



Senior Manager
Joined: 13 Jun 2013
Posts: 276

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Jan 2015, 04:47
Here is an another approach
20^2 =400 thus (x1)^2 = 20^2 (x1)^2  20^2 = 0 now we know that a^2b^2 = (ab)(a+b) here x1 =a and 20=b
thus we have (x120)(x1+20)=0 (x21)(x+19)=0 x=21 or x=19
thus x5=215 =16 or 195 =24



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4261
Location: United States (CA)

If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
07 Jul 2016, 08:33
Bunuel wrote: Walkabout 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 This is an interesting question because our initial instincts tell us to square x 1 by the FOIL method. However, an easier method is to instead take the square root of both sides of the equation. (x  1)^2 = 400 √(x  1)^2 = √400 This gives us: x – 1 = 20 Because there is an expression inside the absolute value sign, we must consider that the entire expression, and not just the variable, can be either positive or negative. We’ll need to solve the equation twice. Solve for x1 as positive: x – 1 = 20 x – 1 = 20 x = 21 Solve for x1 as negative: x – 1 = 20 (x – 1) = 20 x + 1 = 20 x =19 x = 19 Thus, x – 5 can equal either 21 – 5 = 16 or 19 – 5 = 24. Answer is C.
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Manager
Status: On a 600long battle
Joined: 21 Apr 2016
Posts: 138
Location: Hungary
Concentration: Accounting, Leadership
GMAT 1: 410 Q18 V27 GMAT 2: 490 Q35 V23

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Apr 2017, 01:35
Taking the root of both sides is definitely a better approach. Finding the roots of the quadratics can drive one insane! \({ \left( x1 \right) }^{ 2 }=400\\ \sqrt { { \left( x1 \right) }^{ 2 } } =\sqrt { 400 } \\ \left x1 \right =20\\ +\left( x1 \right) =20\quad \leftrightarrow \quad \left( x1 \right) =20\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad or\\ { \left( x1 \right) }^{ 2 }=400\\ \left( x1 \right) \left( x1 \right) =400\)
_________________
"When the going gets tough, the tough gets going!"
Welcoming tips/suggestions/advices (you name it) to help me achieve a 600



Board of Directors
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4271
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Apr 2017, 07:02
Walkabout 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 \((x  1 ) =\) + \(20\) If\(x  1 = +20\) ; \(x = 21 ; So, x  5 = 16\)If \(x  1 = 20\) ; \(x = 19; So, x  5 = 24\)Thus, answer must be (C) 24
_________________
Thanks and Regards
Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
How to use Search Function in GMAT Club  Rules for Posting in QA forum  Writing Mathematical Formulas Rules for Posting in VA forum  Request Expert's Reply ( VA Forum Only )



Director
Joined: 02 Sep 2016
Posts: 683

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
19 Aug 2017, 04:36
(x1)^2= 400 (x1)^2= (20)^2 (x1)^2 (20)^2= 0 Use identity a^2b^2= (a+b)*(ab) (x1+20)(x120)=0 (x+19) (x21)=0 Equate the factorized form to zero. x= 19 or x= 21 Plug in (x5) and check the options. If I took (20)^2 (x1)^2  (20)^2= 0 (x120)* (x1+20)= 0 (x21) (x+19)= 0 x= 21 or x= 19 Same answer. This identity: a^2b^2= (a+b)(ab) comes in handy in many questions.
_________________
Help me make my explanation better by providing a logical feedback.
If you liked the post, HIT KUDOS !!
Don't quit.............Do it.



VP
Joined: 09 Mar 2016
Posts: 1202

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
05 Mar 2018, 03:07
Walkabout 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 I think there is very simple solution to this question no need to do any algebra we can see that (x  1)^2 = 400, the first thought occured to me here (x1)^2 x = should be 21, but from answer choices you can`t see 215 = 16 so the only option is x =  19 (191)^2 which still yields 20 just negative in this case. but negative sign dissapears when raised to even power. hence 195 = 24 so B




Re: If (x  1)^2 = 400 which of the following could be the value &nbs
[#permalink]
05 Mar 2018, 03:07






