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# Question 16, Diagnostic Test, Page, 22 - GMAT 2012

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Intern
Joined: 23 Oct 2012
Posts: 5
Question 16, Diagnostic Test, Page, 22 - GMAT 2012 [#permalink]

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29 Oct 2012, 02:16
Hi,

I am getting stuck with question 16 on page 22 of the GMAT 2012 book, diagnostic section.

I have no math background and currently revamping basic formulas and math vocabulary, however slowly by slowly I gain better understanding of the quantitative section. Though this question I simply cannot figure out. So if anyone could explain to me the most simplified way to calculate these kind of formulas:

Question 16:
Page 22.
Explanation Page: 52

If V3 - 2x = V2x + 1 then, 4x 2 =

What I want to know is the fastest way to calculate this and also where do I start. I understand when to ROOT or SQUARE but do I calculate the root first of V3 for example minus 2?

Sorry for the confusion.

Thanks
Intern
Joined: 10 Oct 2012
Posts: 7
GPA: 3.87
Re: Question 16, Diagnostic Test, Page, 22 - GMAT 2012 [#permalink]

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07 Nov 2012, 17:30
Hi DonCarter,

Usually the book's answer explanations aren't the best or most efficient way to answer the questions for GMAT-purposes, but in this case, it's pretty dead-on. Check the answer explanation on p.53. In general, here are a couple of guidelines that can help you when you see similar problems in the future:

1) When a question asks you to solve for an entire term rather than a single variable, your default reaction should be to try to manipulate the equation in such a way as to solve for that term as a whole. In other words, they're asking you to solve for 4x^2. That should trigger something in your mind that says, "I think I better try to manipulate the equation and see if I can get 4x^2 isolated on one side of the equation. I may or may not be able to, but that's where I'm going to start." What you don't want to do is actually solve for x, then square it, then multiply it by 4

2) When solving equations that contain square roots, it's usually best to square both sides to get rid of the radical. You'll notice that's what they do in Step 1 in the answer explanation. Equations are much easier to work with once you've gotten ride of the radicals.

I hope this helps!

Best,
Brett
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7450
Location: Pune, India
Re: Question 16, Diagnostic Test, Page, 22 - GMAT 2012 [#permalink]

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07 Nov 2012, 21:12
DonCarter wrote:
Hi,

I am getting stuck with question 16 on page 22 of the GMAT 2012 book, diagnostic section.

I have no math background and currently revamping basic formulas and math vocabulary, however slowly by slowly I gain better understanding of the quantitative section. Though this question I simply cannot figure out. So if anyone could explain to me the most simplified way to calculate these kind of formulas:

Question 16:
Page 22.
Explanation Page: 52

If V3 - 2x = V2x + 1 then, 4x 2 =

What I want to know is the fastest way to calculate this and also where do I start. I understand when to ROOT or SQUARE but do I calculate the root first of V3 for example minus 2?

Sorry for the confusion.

Thanks

The given method is pretty much the best way to go about it.
The equation $$\sqrt{3 - 2x} = \sqrt{2x} + 1$$ is satisfied for very few values of x. You need to find what 4x^2 is in case of those values of x. So you manipulate the given equation to get 4x^2.

Mind you, if all options were easy numbers like the first two, I might have quickly put in the values to check whether equation is satisfied or not e.g.
If 4x^2 = 4 (option A), x = 1, -1
If you put x = 1, here: $$\sqrt{3 - 2x} = \sqrt{2x} + 1$$, the equation is not satisfied. So 4x^2 is not 4.

If 4x^2 = 1 (option B), x = 1/2, -1/2
If you put x = 1/2 in the equation, it is again not satisfied.

It's too much work for options with x so the best way to proceed in this question is manipulating the original equation only.
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Re: Question 16, Diagnostic Test, Page, 22 - GMAT 2012 [#permalink]

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08 Nov 2012, 03:36
Expert's post
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DonCarter wrote:
Hi,

I am getting stuck with question 16 on page 22 of the GMAT 2012 book, diagnostic section.

I have no math background and currently revamping basic formulas and math vocabulary, however slowly by slowly I gain better understanding of the quantitative section. Though this question I simply cannot figure out. So if anyone could explain to me the most simplified way to calculate these kind of formulas:

Question 16:
Page 22.
Explanation Page: 52

If V3 - 2x = V2x + 1 then, 4x 2 =

What I want to know is the fastest way to calculate this and also where do I start. I understand when to ROOT or SQUARE but do I calculate the root first of V3 for example minus 2?

Sorry for the confusion.

Thanks

Please post questions in respective forums. This question is discussed here: if-root-3-2x-root-2x-1-then-4x-135539.html

If $$\sqrt{3-2x} = \sqrt{2x} +1$$, then $$4x^2$$ =

(A) 1
(B) 4
(C) 2 − 2x
(D) 4x − 2
(E) 6x − 1

$$\sqrt{3-2x} = \sqrt{2x} +1$$ --> square both sides: $$(\sqrt{3-2x})^2 =(\sqrt{2x} +1)^2$$ --> $$3-2x=2x+2*\sqrt{2x}+1$$ --> rearrange so that to have root at one side: $$2-4x=2*\sqrt{2x}$$ --> reduce by 2: $$1-2x=\sqrt{2x}$$ --> square again: $$(1-2x)^2=(\sqrt{2x})^2$$ --> $$1-4x+4x^2=2x$$ --> rearrange again: $$4x^2=6x-1$$.

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Re: Question 16, Diagnostic Test, Page, 22 - GMAT 2012   [#permalink] 08 Nov 2012, 03:36
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