Find all School-related info fast with the new School-Specific MBA Forum

It is currently 20 Aug 2014, 20:55

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the value of x? 1. 2x + 1 = 0 2. (x+1)^2 =

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 15 Nov 2009
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 1

What is the value of x? 1. 2x + 1 = 0 2. (x+1)^2 = [#permalink] New post 21 Nov 2009, 12:12
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

67% (01:43) correct 33% (00:00) wrong based on 4 sessions
What is the value of x?
1. 2x + 1 = 0
2. (x+1)^2 = x^2

The OG says that the second equation can be solved by expanding the squares and reducing it to 2x +1 = 0 thereby making it sufficient to solve. My question is why can't we solve it like this?

(x+1)^2 = x^2
Square root both sides and you get
(x+1) = x
subtract x from both sides to get
1 = 0
The equation now is unsolvable and therefore I guess insufficient.

Thanks
Manager
Manager
avatar
Joined: 29 Jul 2009
Posts: 121
Followers: 2

Kudos [?]: 13 [0], given: 23

Re: What is the value of x (OG DS question no. 29) [#permalink] New post 21 Nov 2009, 12:32
groovy261 wrote:
What is the value of x?
1. 2x + 1 = 0
2. (x+1)^2 = x^2

The OG says that the second equation can be solved by expanding the squares and reducing it to 2x +1 = 0 thereby making it sufficient to solve. My question is why can't we solve it like this?

(x+1)^2 = x^2
Square root both sides and you get
(x+1) = x
subtract x from both sides to get
1 = 0
The equation now is unsolvable and therefore I guess insufficient.

Thanks



u cant take squareroot of both sides and not consider both the signs i.e if X^2 = 16 then x= 4 or x = -4
same rule applies to the equation in the second statement.

expanding is a better method of solving it for x

X^2 + 2X + 1 = X^2
i.e 2X + 1 = 0..this is nothing but statement 1 and now u can solve for X.

OR

|X+1| = |X|...but this will comsume time!!

HTH
1 KUDOS received
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 967
Location: Toronto
Followers: 253

Kudos [?]: 652 [1] , given: 3

GMAT Tests User
Re: What is the value of x (OG DS question no. 29) [#permalink] New post 21 Nov 2009, 12:40
1
This post received
KUDOS
groovy261 wrote:
What is the value of x?
1. 2x + 1 = 0
2. (x+1)^2 = x^2

The OG says that the second equation can be solved by expanding the squares and reducing it to 2x +1 = 0 thereby making it sufficient to solve. My question is why can't we solve it like this?

(x+1)^2 = x^2
Square root both sides and you get
(x+1) = x
subtract x from both sides to get
1 = 0
The equation now is unsolvable and therefore I guess insufficient.

Thanks


You cannot simply take square roots on both sides, because \sqrt{x^2} is not necessarily equal to x. Indeed, as you've shown, if they were always equal the equation could not possibly have any solutions, but it does: x = -1/2. In general:

\begin{align*}
\sqrt{x^2} &= x \text{ if } x \geq 0 \\
\sqrt{x^2} &= -x \text{ if } x < 0
\end{align*}


You might try this with an example negative number. Taking -3, for example, notice that \sqrt{(-3)^2} is not equal to -3; it's equal to \sqrt{9} = 3, which is the same thing as -(-3).

Knowing this, it becomes possible to answer the question by taking square roots on both sides, though the approach taken in the OG (expanding both sides) would be more straightforward. Still, if we want to take roots on both sides:

Just glancing at the equation in Statement 2, it may be clear that x and x+1 cannot both be positive; the equation would make no sense, since (x+1)^2 would certainly be larger than x. Similarly, x and x+1 cannot both be negative. So one of them must be negative, the other positive, and since x is smaller than x+1, x must be negative and x+1 must be positive. Since x must be negative, \sqrt{x^2} = -x. Now we can take square roots, knowing what sign we will need for each:

\begin{align*}
(x+1)^2 &= x^2 \\
\sqrt{(x+1)^2} &= \sqrt{x^2} \\
x+1 &= -x \\
x &= \frac{-1}{2}
\end{align*}

_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

1 KUDOS received
Manager
Manager
avatar
Joined: 19 Nov 2007
Posts: 228
Followers: 1

Kudos [?]: 80 [1] , given: 1

GMAT Tests User
Re: What is the value of x (OG DS question no. 29) [#permalink] New post 22 Nov 2009, 04:39
1
This post received
KUDOS
groovy261 wrote:
What is the value of x?
1. 2x + 1 = 0
2. (x+1)^2 = x^2

The OG says that the second equation can be solved by expanding the squares and reducing it to 2x +1 = 0 thereby making it sufficient to solve. My question is why can't we solve it like this?

(x+1)^2 = x^2
Square root both sides and you get
(x+1) = x
subtract x from both sides to get
1 = 0
The equation now is unsolvable and therefore I guess insufficient.

Thanks


(x+1)^2=x^2 is equal to (x+1)=x or (x+1)=-x; In the first case the equation is not valid; But the second case the equation is valid and x=-1/2
Intern
Intern
avatar
Joined: 15 Nov 2009
Posts: 6
Followers: 0

Kudos [?]: 0 [0], given: 1

Re: What is the value of x (OG DS question no. 29) [#permalink] New post 22 Nov 2009, 13:39
Thank you all for helping me out. I have now understood the it better.
Re: What is the value of x (OG DS question no. 29)   [#permalink] 22 Nov 2009, 13:39
    Similar topics Author Replies Last post
Similar
Topics:
What is the value of 5x^2+4x-1? (1) x(x+2)=0 (2) x=0 tarek99 2 18 Aug 2008, 05:51
What is the value of 5x2 + 4x 1? (1) x(x + 2)= 0 (2) x= 0 marcodonzelli 1 12 Mar 2008, 12:12
What is the value of x? (1) (x + 2)(x + 3) = 0 (2) (x^2) + JustinTI 4 06 Aug 2007, 18:34
What is the value of X^2 -Y^2? 1. x+y=2x 2. x+y=0 I jamesrwrightiii 4 17 Jul 2006, 20:59
What is the value of x? 1) x^3-x=0 2) x^2-x=0 I realize the willgoldberg 4 05 Feb 2005, 15:19
Display posts from previous: Sort by

What is the value of x? 1. 2x + 1 = 0 2. (x+1)^2 =

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.