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 =

ANSWER is E (6x -1)

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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