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

 It is currently 23 Oct 2019, 21:52 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.  Which value(s) of x satisfies the equation above?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

3
12 00:00

Difficulty:   65% (hard)

Question Stats: 55% (01:34) correct 45% (01:37) wrong based on 464 sessions

HideShow timer Statistics

$$2x - 2 = \sqrt{3x^2+13}$$

Which value(s) of x satisfies the equation above?

I. -1
II. 4
III. 9

(A) I
(B) III
(C) I & II
(D) I & III
(E) I, II, & III

For a discussion of algebraic equations involving radicals, as well as a solution to this question, see this post:

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
VP  Status: Far, far away!
Joined: 02 Sep 2012
Posts: 1019
Location: Italy
Concentration: Finance, Entrepreneurship
GPA: 3.8
Re: Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

3
Using numbers:

$$2x - 2 = \sqrt{3x^2+13}$$

I)-1

$$-4= \sqrt{3(-1)^2+13}$$

$$\sqrt{3+13}$$ does not equal $$-4$$ , so $$-1$$ is NOT a possible value.

If we take a look at the possible answer, all contain I except B. So B is the correct answer
_________________
It is beyond a doubt that all our knowledge that begins with experience.
Kant , Critique of Pure Reason

Tips and tricks: Inequalities , Mixture | Review: MGMAT workshop
Strategy: SmartGMAT v1.0 | Questions: Verbal challenge SC I-II- CR New SC set out !! , My Quant

Rules for Posting in the Verbal Forum - Rules for Posting in the Quant Forum[/size][/color][/b]
Math Expert V
Joined: 02 Sep 2009
Posts: 58471
Re: Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

1
mikemcgarry wrote:
$$2x - 2 = \sqrt{3x^2+13}$$

Which value(s) of x satisfies the equation above?

I. -1
II. 4
III. 9

(A) I
(B) III
(C) I & II
(D) I & III
(E) I, II, & III

For a discussion of algebraic equations involving radicals, as well as a solution to this question, see this post:

Mike Similar question to practice: new-algebra-set-149349-60.html#p1200948
_________________
SVP  Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1746
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

1
I solved the equation to get the wrong answer. Squaring both sides made the difference.

Leason Learnt: Such type of questions, better to place the given values & check.
_________________
Kindly press "+1 Kudos" to appreciate Manager  Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

1
mikemcgarry wrote:
$$2x - 2 = \sqrt{3x^2+13}$$

Which value(s) of x satisfies the equation above?

I. -1
II. 4
III. 9

(A) I
(B) III
(C) I & II
(D) I & III
(E) I, II, & III

For a discussion of algebraic equations involving radicals, as well as a solution to this question, see this post:

Mike $$2x-2 = \sqrt{3x^2 + 13}$$

Squaring both sides, we get

$$4x^2 - 4x + 3 = 3x^2 + 13$$

$$x^2 - 4x = 9$$

$$x (x-4) = 9$$

x = 9 or x-4 = 9

x = 9 or x = 13

Since only X = 9 is given and it satisfies the condition
Intern  Joined: 02 Jul 2014
Posts: 24
Location: United States
GPA: 3.24
WE: Engineering (Computer Software)
Re: Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

2
Ashishmathew01081987 wrote:
mikemcgarry wrote:
$$2x - 2 = \sqrt{3x^2+13}$$

Which value(s) of x satisfies the equation above?

I. -1
II. 4
III. 9

(A) I
(B) III
(C) I & II
(D) I & III
(E) I, II, & III

For a discussion of algebraic equations involving radicals, as well as a solution to this question, see this post:

Mike $$2x-2 = \sqrt{3x^2 + 13}$$

Squaring both sides, we get

$$4x^2 - 4x + 3 = 3x^2 + 13$$

$$x^2 - 4x = 9$$

$$x (x-4) = 9$$

x = 9 or x-4 = 9

x = 9 or x = 13

Since only X = 9 is given and it satisfies the condition

Hey Ashishmathew,
(2x-2)^2 = 4x^2 +4-8x right ? How come ur LHS of the eqn is [m][b]4x^2 - 4x + 3 ? Or Am I missing out something here ?
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

3
sreelakshmigs wrote:
Ashishmathew01081987 wrote:
mikemcgarry wrote:
$$2x - 2 = \sqrt{3x^2+13}$$

Which value(s) of x satisfies the equation above?

I. -1
II. 4
III. 9

(A) I
(B) III
(C) I & II
(D) I & III
(E) I, II, & III

For a discussion of algebraic equations involving radicals, as well as a solution to this question, see this post:

Mike $$2x-2 = \sqrt{3x^2 + 13}$$

Squaring both sides, we get

$$4x^2 - 4x + 3 = 3x^2 + 13$$

$$x^2 - 4x = 9$$

$$x (x-4) = 9$$

x = 9 or x-4 = 9

x = 9 or x = 13

Since only X = 9 is given and it satisfies the condition

Hey Ashishmathew,
(2x-2)^2 = 4x^2 +4-8x right ? How come ur LHS of the eqn is $$4x^2 - 4x + 3$$ ? Or Am I missing out something here ?

Dear sreelakshmigs
I'm happy to respond. First of all, Ashishmathew01081987's solution is not correct at all. You are perfectly correct:
$$(2x-2)^2 = 4x^2 - 8x + 4$$
Also, the factoring thing he does at the end, the steps after x(x - 4) = 9, are 100% incorrect.
If you want to see the correct solution to this problem, see:

Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Manager  Status: I am not a product of my circumstances. I am a product of my decisions
Joined: 20 Jan 2013
Posts: 108
Location: India
Concentration: Operations, General Management
GPA: 3.92
WE: Operations (Energy and Utilities)
Re: Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

Hey Ashishmathew,
(2x-2)^2 = 4x^2 +4-8x right ? How come ur LHS of the eqn is $$4x^2 - 4x + 3$$ ? Or Am I missing out something here ?[/quote]
Dear sreelakshmigs
I'm happy to respond. First of all, Ashishmathew01081987's solution is not correct at all. You are perfectly correct:
$$(2x-2)^2 = 4x^2 - 8x + 4$$
Also, the factoring thing he does at the end, the steps after x(x - 4) = 9, are 100% incorrect.
If you want to see the correct solution to this problem, see:

Mike [/quote]

Thanks Sree for pointing out my mistake. That was a blunder. Hope that it doesn't happen on the GMAT.

Thanks Mike, I understand why the factoring stuff would have led me into the trap. Plugging numbers is the best option here.
Magoosh GMAT Instructor G
Joined: 28 Dec 2011
Posts: 4472
Re: Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

Ashishmathew01081987 wrote:
Thanks Sree for pointing out my mistake. That was a blunder. Hope that it doesn't happen on the GMAT.

Thanks Mike, I understand why the factoring stuff would have led me into the trap. Plugging numbers is the best option here.

Dear Ashishmathew01081987,
Actually, it's very good to understand the algebra in this problem. Again, you can see a full algebraic solution at the blog to which I linked. Plugging numbers is good sometimes, but it's best not to make that a one-size-fit-all kind of strategy.
Does this make sense?
Mike _________________
Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
Intern  B
Joined: 17 Jul 2017
Posts: 4
Which value(s) of x satisfies the equation above?  [#permalink]

Show Tags

Zarrolou wrote:
Using numbers:

$$2x - 2 = \sqrt{3x^2+13}$$

I)-1

$$-4= \sqrt{3(-1)^2+13}$$

$$\sqrt{3+13}$$ does not equal $$-4$$ , so $$-1$$ is NOT a possible value.

If we take a look at the possible answer, all contain I except B. So B is the correct answer

I think this might be incorrect.

First, -4 = 16^(1/2) is as correct answer since (-4)(-4) = 16.
Second, the bold part is not correct. x² when x = -1 is the same as -1² = -1 and not (-1)² = 1, so we should have -4 = 10^(1/2). So, option I is incorrect.
Since the only option that says I is incorrect is B, then, B is our answer.
Non-Human User Joined: 09 Sep 2013
Posts: 13418
Re: Which value(s) of x satisfies the equation above?  [#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: Which value(s) of x satisfies the equation above?   [#permalink] 25 Nov 2018, 09:24
Display posts from previous: Sort by

Which value(s) of x satisfies the equation above?

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

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