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

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

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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

Mike :-)
[Reveal] Spoiler: OA

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New post 09 May 2013, 11:27
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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
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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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

Mike :-)


Similar question to practice: new-algebra-set-149349-60.html#p1200948
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Re: Which value(s) of x satisfies the equation above? [#permalink]

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New post 10 May 2013, 01:55
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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.
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Which value(s) of x satisfies the equation above? [#permalink]

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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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

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
Answer is B

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Re: Which value(s) of x satisfies the equation above? [#permalink]

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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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

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
Answer is B



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 ?

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New post 03 Nov 2014, 11:00
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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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

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
Answer is B


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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

Mike :-)
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New post 03 Nov 2014, 21:48
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:
http://magoosh.com/gmat/2013/gmat-math- ... -radicals/

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.

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New post 03 Nov 2014, 22:34
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 :-)
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Re: Which value(s) of x satisfies the equation above? [#permalink]

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Hello from the GMAT Club BumpBot!

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Which value(s) of x satisfies the equation above? [#permalink]

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New post 12 Nov 2017, 10:24
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.

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Which value(s) of x satisfies the equation above?   [#permalink] 12 Nov 2017, 10:24
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