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{x} denotes the integer nearest to x. For example,

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by Max@Math Revolution » Tue Mar 17, 2020 2:06 am
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[GMAT math practice question]

{x} denotes the integer nearest to x. For example, {2.7} = 3, {-3.4} = -3. What is the value of \(\left\{\frac{\sqrt{3}}{\sqrt{3}+2}\right\}+\left\{\frac{\sqrt{3}}{\sqrt{3}-2}\right\}\) ?

A.3
B.4
C. 5
D. 6
E.7
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Re: {x} denotes the integer nearest to x. For example,

by Max@Math Revolution » Thu Mar 19, 2020 1:50 am
=>

\(\frac{\sqrt{3}}{\sqrt{3}+2}\)

= \(\frac{\sqrt{3}\left(2-\sqrt{3}\right)}{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\)
= \(\frac{2\sqrt{3}-3}{4-3}\)
= \(2\sqrt{3}-3\)
2*1.7-3 = 0.4

\(\frac{\sqrt{3}}{\sqrt{3}-2}\)
= \(\frac{\sqrt{3}\left(\sqrt{3}+2\right)}{\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)}\)
= \(\frac{3+2\sqrt{3}}{3-4}\)
= -3-2 \(\sqrt{3}\)
-3-2*1.7=-3-3.4=-6.4

\(\left\{\frac{\sqrt{3}}{\sqrt{3}+2}\right\}+\left\{\frac{\sqrt{3}}{\sqrt{3}-2}\right\}\)
={0.4}-{-6.4}
=0-(-6)=6

Therefore, D is the answer.
Answer: D
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