Oct 18 08:00 AM PDT  09:00 AM PDT Learn an intuitive, systematic approach that will maximize your success on Fillintheblank GMAT CR Questions. Oct 19 07:00 AM PDT  09:00 AM PDT Does GMAT RC seem like an uphill battle? eGMAT is conducting a free webinar to help you learn reading strategies that can enable you to solve 700+ level RC questions with at least 90% accuracy in less than 10 days. Sat., Oct 19th at 7 am PDT Oct 20 07:00 AM PDT  09:00 AM PDT Get personalized insights on how to achieve your Target Quant Score. Oct 22 08:00 PM PDT  09:00 PM PDT On Demand for $79. For a score of 4951 (from current actual score of 40+) AllInOne Standard & 700+ Level Questions (150 questions) Oct 23 08:00 AM PDT  09:00 AM PDT Join an exclusive interview with the people behind the test. If you're taking the GMAT, this is a webinar you cannot afford to miss!
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 173

If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
20 Dec 2012, 09:07
Question Stats:
74% (01:12) correct 26% (01:34) wrong based on 917 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: 58402

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




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, 10:36
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: 13 Feb 2011
Posts: 79

If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
30 Jul 2014, 09:33
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: 22

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Dec 2014, 23:04
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: 266

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
09 Dec 2014, 02:15
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: 22

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
09 Dec 2014, 04:24
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: 402
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, 08:58
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: 15263
Location: United States (CA)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
06 Jan 2015, 11:17
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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
06 Jan 2015, 11:28
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
_________________
Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★



SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1749
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, 02:41
\((x  1)^2 = 400\) \(x  1 = \pm 20\) \(x = 1 \pm 20 = 21 OR 19\) x  5 = 215 = 16 OR 195 = 24 Answer = C
_________________
Kindly press "+1 Kudos" to appreciate



Senior Manager
Joined: 13 Jun 2013
Posts: 266

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
08 Jan 2015, 05:47
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: 8085
Location: United States (CA)

If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
07 Jul 2016, 09:33
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.
_________________
5star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews If you find one of my posts helpful, please take a moment to click on the "Kudos" button.



Manager
Status: On a 600long battle
Joined: 22 Apr 2016
Posts: 136
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, 02:35
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: 4775
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, 08:02
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
_________________



Director
Joined: 02 Sep 2016
Posts: 649

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
19 Aug 2017, 05:36
(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: 1230

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
05 Mar 2018, 04:07
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



SVP
Joined: 03 Jun 2019
Posts: 1699
Location: India

Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
Show Tags
14 Aug 2019, 23:47
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 Given: (x  1)^2 = 400 Asked: Which of the following could be the value of x  5? x1 = +20 x5 = +20 4 x 5 = 204 or 204 => 16 or 24 IMO C
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com




Re: If (x  1)^2 = 400 which of the following could be the value
[#permalink]
14 Aug 2019, 23:47






