GMATClub Test M12 Q1 - Faster method?

Question

Hi all

\frac{1}{2+\sqrt{3}}=?

A.  \sqrt{3}-2 
B.  2-\sqrt{3} 
C.  \sqrt{2}+\sqrt{3} 
D.  2+\sqrt{3} 
E.  \sqrt{3}+4

B
Solution: (2-\sqrt{3})*(2+\sqrt{3})=4-3=1

Is there a fast way to recognize which one is correct here? Or can some one elaborate on the solution?

Thanks!

edit: corrected answer choice. whoops.

Bunuel · Answer

Answer can not be D, it should be B. The question is about the application of formula:  a^2-b^2=(a-b)(a+b) . Basically what we want to do is to make denominator 1, as no answer choice is in the form of fraction.

How can we do that?

Multiply  \frac{1}{2+\sqrt{3}}  by  \frac{2-\sqrt{3}}{2-\sqrt{3}} , which is 1, so that won't affect the value of our fraction. We'll get:  \frac{1}{2+\sqrt{3}}*\frac{2-\sqrt{3}}{2-\sqrt{3}}=\frac{2-\sqrt{3}}{2^2-\sqrt{3}^2}=\frac{2-\sqrt{3}}{4-3}=2-\sqrt{3}

Answer: B.

chix475ntu · Answer

Answer should be B. Is it gmatclub test with the wrong answer? hmmmm :shock:

brentbrent · Answer

Whoops. 
Answer is B. I have to edit that, gmat club isn't wrong =-)

brentbrent · Answer

Thanks Bunnel. I didn't even think about that formula..sheesh.
cheers

bangalorian2000 · Answer

Answer is B

Multiply numerator & denominator by 2-\sqrt{3}.

Bullet · Answer

20 sec question and answer must be B.

multiply numerator and denominator by 2-\sqrt{3}

Cheers!

Crushit · Answer

How do you go from 2- 3/4-3 to the final answer?

Bullet · Answer

just simplify it

2 - sqrt(3) / 4 - 3

= 2 - sqrt(3)/1

= 2 - sqrt(3) which is the answer

mustdoit · Answer

Try this method instead....

we knw sqaure root of 3 is 1.732

So the equation becomes 1/(2+1.732)
that gives 1/(3.732) or may be rounded off to 1/4 or 0.25

Now working with options only B gives 2-1.732 that would give answer as 0.25.

Hope this helps.

GMATClub Test M12 Q1 - Faster method?

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