GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 17 Oct 2019, 10:57 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  If (x - 1)^2 = 400 which of the following could be the value

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
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

3
20 00:00

Difficulty:   25% (medium)

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
Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Re: If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

4
2
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

$$(x - 1)^2 = 400$$ --> $$x-1=20$$ or $$x-1=-20$$ --> $$x-5=20-4=16$$ or $$x-5=-20-4=-24$$.

_________________
General Discussion
Intern  Joined: 21 Jan 2014
Posts: 11
Location: Germany
Concentration: Entrepreneurship, Strategy
GMAT Date: 05-28-2014
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

1
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  B
Joined: 13 Feb 2011
Posts: 79
If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

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

1
Bunuel 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

$$(x - 1)^2 = 400$$ --> $$x-1=20$$ or $$x-1=-20$$ --> $$x-5=20-4=16$$ or $$x-5=-20-4=-24$$.

Hi there, where did the -4 come from? i.e.
$$x-5=20-4=16$$ or $$x-5=-20-4=-24$$

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

ColdSushi wrote:
Bunuel 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

$$(x - 1)^2 = 400$$ --> $$x-1=20$$ or $$x-1=-20$$ --> $$x-5=20-4=16$$ or $$x-5=-20-4=-24$$.

Hi there, where did the -4 come from? i.e.
$$x-5=20-4=16$$ or $$x-5=-20-4=-24$$

Thanks.

hi, remember we have calculated the value of x-1=20 or -20. ------------1)
x-5 = (x-1)-4 now from 1, put the value of x-1 as 20 or -20
= 20-4 =16
or x-5 = (x-1)-4 = -20-4 = -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

Hi there, where did the -4 come from? i.e.
$$x-5=20-4=16$$ or $$x-5=-20-4=-24$$

Thanks.[/quote]

hi, remember we have calculated the value of x-1=20 or -20. ------------1)
x-5 = (x-1)-4 now from 1, put the value of x-1 as 20 or -20
= 20-4 =16
or x-5 = (x-1)-4 = -20-4 = -24

i hope it helps.[/quote]

Yep great - understand now. Appreciate your help!
Senior Manager  Status: Math is psycho-logical
Joined: 07 Apr 2014
Posts: 402
Location: Netherlands
GMAT Date: 02-11-2015
WE: Psychology and Counseling (Other)
Re: If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

1
1
Could we also solve this like this:

(x-1)^2 = (x-1)(x-1)?

I tried like this at first, but didn't end up well.. Unless I miscalculated sth somewhere.

Thank you.
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

3
1
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. 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
_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15263
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

3
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....

(X-1)^2 = 400
(X-1)(X-1) = 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
_________________
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

1
1
$$(x - 1)^2 = 400$$

$$x - 1 = \pm 20$$

$$x = 1 \pm 20 = 21 OR -19$$

x - 5 = 21-5 = 16 OR -19-5 = -24

_________________
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

Here is an another approach

20^2 =400
thus (x-1)^2 = 20^2
(x-1)^2 - 20^2 = 0
now we know that a^2-b^2 = (a-b)(a+b)
here x-1 =a and 20=b

thus we have
(x-1-20)(x-1+20)=0
(x-21)(x+19)=0
x=21 or x=-19

thus x-5=21-5 =16 or -19-5 =-24
Target Test Prep Representative D
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

3
1
Bunuel 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 x-1 as positive:

|x – 1| = 20

x – 1 = 20

x = 21

Solve for x-1 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.

_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

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  S
Status: On a 600-long battle
Joined: 22 Apr 2016
Posts: 136
Location: Hungary
Schools: Erasmus '19
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

Taking the root of both sides is definitely a better approach. Finding the roots of the quadratics can drive one insane! $${ \left( x-1 \right) }^{ 2 }=400\\ \sqrt { { \left( x-1 \right) }^{ 2 } } =\sqrt { 400 } \\ \left| x-1 \right| =20\\ +\left( x-1 \right) =20\quad \leftrightarrow \quad -\left( x-1 \right) =20\\ \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad or\\ { \left( x-1 \right) }^{ 2 }=400\\ \left( x-1 \right) \left( x-1 \right) =400$$
_________________
"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 D
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

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  G
Joined: 02 Sep 2016
Posts: 649
Re: If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

(x-1)^2= 400
(x-1)^2= (20)^2

(x-1)^2 -(20)^2= 0

Use identity a^2-b^2= (a+b)*(a-b)

(x-1+20)(x-1-20)=0
(x+19) (x-21)=0

Equate the factorized form to zero.

x= -19 or x= 21

Plug in (x-5) and check the options.

If I took (-20)^2

(x-1)^2 - (-20)^2= 0

(x-1-20)* (x-1+20)= 0

(x-21) (x+19)= 0

x= 21 or x= -19

This identity: a^2-b^2= (a+b)(a-b) 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  D
Joined: 09 Mar 2016
Posts: 1230
Re: If (x - 1)^2 = 400 which of the following could be the value  [#permalink]

Show Tags

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 (x-1)^2 x = should be 21, but from answer choices you can`t see 21-5 = 16
so the only option is x = - 19 (-19-1)^2 which still yields -20 just negative in this case. but negative sign dissapears when raised to even power.

hence -19-5 = -24

so B SVP  P
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

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?

x-1 = +-20

x-5 = +-20 -4

x- 5 = 20-4 or -20-4 => 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 Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com Re: If (x - 1)^2 = 400 which of the following could be the value   [#permalink] 14 Aug 2019, 23:47
Display posts from previous: Sort by

If (x - 1)^2 = 400 which of the following could be the value

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  