Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 18 Jul 2019, 14:39 ### 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-2=x+2 , x=?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42 GPA: 3.82

### Show Tags

1
12 00:00

Difficulty:   65% (hard)

Question Stats: 60% (01:55) correct 40% (02:53) wrong based on 117 sessions

### HideShow timer Statistics If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2\sqrt{3}$$

Original Version wrote:
If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2[fraction]3[/fraction]$$

_________________

Originally posted by MathRevolution on 12 Jul 2017, 02:06.
Last edited by broall on 12 Jul 2017, 20:57, edited 2 times in total.
Fixed typo
Director  D
Joined: 13 Mar 2017
Posts: 731
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

9
3
MathRevolution wrote:
If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2[fraction]3[/fraction]$$

$$x-2=\sqrt{x}+\sqrt{2}$$
$$(\sqrt{x}-\sqrt{2} )(\sqrt{x}+\sqrt{2}) = (\sqrt{x}+\sqrt{2})$$
$$\sqrt{x}-\sqrt{2}-1 = 0$$
$$\sqrt{x} = 1+\sqrt{2}$$
$$x = 3 +2\sqrt{2}$$

_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu

Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)

What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
##### General Discussion
Director  G
Joined: 02 Sep 2016
Posts: 657
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

MathRevolution

This is how I started solving this question but don't know how to solve it further..

x-sq.root x= 2+sq.root 2
Squaring both the sides

x^2+ x- 2x*sq.root x= 2+4+4*sq.root 2

x^2-x*sq.root x= 6+4* sq.root 2

x(x- sq.root x)= 2(3+2* sq.root 2)

_________________
Help me make my explanation better by providing a logical feedback.

If you liked the post, HIT KUDOS !!

Don't quit.............Do it.
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3360
Location: India
GPA: 3.12
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

1
MathRevolution wrote:
If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2[fraction]3[/fraction]$$

MathRevolution
Please correct the formatting for Option E. if you meant it to be $$2+2\sqrt{3}$$

As for the solution :

Since $$x-2=\sqrt{x}+\sqrt{2}$$, we can rewrite the statement to be $$x - \sqrt{x} = 2 + \sqrt{2}$$
Because $$\sqrt{2}$$ = 1.4(approximately) , the value of $$x - \sqrt{x}$$ = 2 + $$\sqrt{2}$$ = 2 +1.4 = 3.4

Option A, if x = $$3+2\sqrt{2}$$, the value of x = 3 + 2*1.4 = 3 + 2.8 = 5.8

Now using this value of x in the expression $$x - \sqrt{x}$$,

$$x - \sqrt{x} = 5.8 - \sqrt{5.8} = 5.8 - 2.4 = 3.4$$ because $$2.4^2 = 5.76$$ which is closest to 5.8

Hence, making Option A our correct answer!
_________________
You've got what it takes, but it will take everything you've got
Manager  B
Joined: 04 May 2014
Posts: 158
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

Solution given by pushpitkc is the best approach.

It can also be solved by plugin

$$X=3+2(2)ˆ1/2$$

$$3+2(2)ˆ1/2-2=(3+2(2)ˆ1/2)ˆ1/2+(2)ˆ1/2$$

$$1+2(2)ˆ1/2-(2)ˆ1/2=(3+2(2)ˆ1/2)ˆ1/2$$

$$(1+(2)ˆ1/2)ˆ2=3+2(2)ˆ1/2$$-Squaring both the sides

$$(1)ˆ2+2(2)ˆ1/2+2=3+2(2)ˆ1/2$$
$$3+2(2)ˆ1/2=3+2(2)ˆ1/2$$
Director  G
Joined: 02 Sep 2016
Posts: 657
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

pushpitkc wrote:
MathRevolution wrote:
If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2[fraction]3[/fraction]$$

MathRevolution
Please correct the formatting for Option E. if you meant it to be $$2+2\sqrt{3}$$

As for the solution :

Since $$x-2=\sqrt{x}+\sqrt{2}$$, we can rewrite the statement to be $$x - \sqrt{x} = 2 + \sqrt{2}$$
Because $$\sqrt{2}$$ = 1.4(approximately) , the value of $$x - \sqrt{x}$$ = 2 + $$\sqrt{2}$$ = 2 +1.4 = 3.4

Option A, if x = $$3+2\sqrt{2}$$, the value of x = 3 + 2*1.4 = 3 + 2.8 = 5.8

Now using this value of x in the expression $$x - \sqrt{x}$$,

$$x - \sqrt{x} = 5.8 - \sqrt{5.8} = 5.8 - 2.4 = 3.4$$ because $$2.4^2 = 5.76$$ which is closest to 5.8

Hence, making Option A our correct answer!

Great method.

Squaring both the sides is a very time consuming approach.

Also if there was some other value instead of sq.root 2, may be sq.root 7 or 11......How will we solve then? Should we learn the sq.roots?

Thanks
Intern  Joined: 30 Jun 2017
Posts: 3
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

MathRevolution wrote:
If $$x-2=\sqrt{x}+\sqrt{2}$$ , x=?

A. $$3+2\sqrt{2}$$
B. $$3-2\sqrt{2}$$
C. $$3+\sqrt{2}$$
D. $$3-\sqrt{2}$$
E. $$2+2[fraction]3[/fraction]$$

I Couldn't figure out the solution at first. But, later understood that this can be solved by rewriting the LHS as (a+b)*(a-b).

As pointed out in previous post. Good question- Thanks for posting.
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 7603
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

==> You get x-2=√x+√2 , (√x-√2)(√x+√2)= √x+√2. If you divide √x+√2 on both sides, you get √x-√2=1, then √x=√2+1. Then, if you square both sides, you get x=(√2+1)^2=2+1+2√2 =3+2√2.

_________________
Intern  B
Joined: 19 Jan 2014
Posts: 35
Schools: Melbourne '20
GMAT 1: 670 Q45 V37 Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

1
x-2 = √x+√2
Use conjugate for √x+√2 = √x-√2

x-2 = (√x+√2) (√x-√2)/(√x-√2)

x-2 = (x-2)/(√x-√2)

√x-√2 = 1

√x = 1+√2

x = (1+√2)^2

x = 3+2√2 ---- Option A
Non-Human User Joined: 09 Sep 2013
Posts: 11702
Re: If x-2=x+2 , x=?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: If x-2=x+2 , x=?   [#permalink] 22 Dec 2018, 02:18
Display posts from previous: Sort by

# If x-2=x+2 , x=?  