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Updated on: 16 Oct 2022, 00:16
Originally posted by MathRevolution on 17 Mar 2020, 03:08.
Last edited by chetan2u on 16 Oct 2022, 00:16, edited 2 times in total.
Last edited by chetan2u on 16 Oct 2022, 00:16, edited 2 times in total.
Corrected the question
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
54% (02:02) correct
46%
(02:11)
wrong
based on 207
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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 \(\{\frac{\sqrt{3}}{\sqrt{3}+2}\} + \{\frac{\sqrt{3}}{\sqrt{3}-2}\}? \)
A.\(6\)
B.\(0\)
C. \(-5\)
D. \(-6\)
E.\(-7\)
\(\{x\}\) denotes the integer nearest to \(x\). For example, \(\{2.7\} = 3, \{-3.4\} = -3\). What is the value of \(\{\frac{\sqrt{3}}{\sqrt{3}+2}\} + \{\frac{\sqrt{3}}{\sqrt{3}-2}\}? \)
A.\(6\)
B.\(0\)
C. \(-5\)
D. \(-6\)
E.\(-7\)
18 Mar 2020, 22:40
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MathRevolution
The question is FAULTY..
If \({2.7} = 3, {-3.4} = -3\), then \(\sqrt{3}=1.732=2\)...
\({\frac{\sqrt{3}}{\sqrt{3}+2}} + {\frac{\sqrt{3}}{\sqrt{3}-2}}= \)
\(\frac{2}{2+2}+\frac{2}{2-2}\)..
The denominator cannot be 0... So NOT possible...
How ever I believe it is meant that entire term is x and we have to find the answer after simplifying the term..
\({\frac{\sqrt{3}}{\sqrt{3}+2}} + {\frac{\sqrt{3}}{\sqrt{3}-2}}=\frac{\sqrt{3}*(\sqrt{3}-2)+\sqrt{3}*(\sqrt{3}+2)}{(\sqrt{3}+2)(\sqrt{3}-2)}=\frac{6}{\sqrt{3}^2-2^2} =\frac{6}{3-4}=-6\)
So, the answer should be -6, but that is NOT in the choices..
For the answer to be 6, the question should have been..
What is the value of x if x= \({\frac{\sqrt{3}}{\sqrt{3}+\sqrt{2}}} + {\frac{\sqrt{3}}{\sqrt{3}-\sqrt{2}}}? \)
General Discussion
19 Mar 2020, 03:54
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=>
\(\frac{\sqrt{3}}{\sqrt{3}+2}\)
\(=\frac{\sqrt{3}(2-\sqrt{3})}{(2+\sqrt{3})(2-\sqrt{3})}\)
\(=\frac{2\sqrt{3}-3}{4-3}\)
\(= 2\sqrt{3}-3\)
\(≒2*1.7-3 = 0.4\)
\(\frac{\sqrt{3}}{\sqrt{3}-2}\)
\(=\frac{\sqrt{3}((\sqrt{3}+2)}{(\sqrt{3}-2)(\sqrt{3}+2)}\)
\(=\frac{3+2\sqrt{3}}{3-4}\)
\(= -3 - 2√3\)
\(≒ -3 – 2*1.7 = -3 – 3.4 = -6.4\)
\(\{\frac{\sqrt{3}}{\sqrt{3}+2}\}+\{\frac{\sqrt{3}}{{\sqrt{3}-2}}\}\)
\(= \{0.4\} – \{-6.4\}\)
\(= 0 – (-6) = 6.\)
Therefore, D is the answer.
Answer: D
\(\frac{\sqrt{3}}{\sqrt{3}+2}\)
\(=\frac{\sqrt{3}(2-\sqrt{3})}{(2+\sqrt{3})(2-\sqrt{3})}\)
\(=\frac{2\sqrt{3}-3}{4-3}\)
\(= 2\sqrt{3}-3\)
\(≒2*1.7-3 = 0.4\)
\(\frac{\sqrt{3}}{\sqrt{3}-2}\)
\(=\frac{\sqrt{3}((\sqrt{3}+2)}{(\sqrt{3}-2)(\sqrt{3}+2)}\)
\(=\frac{3+2\sqrt{3}}{3-4}\)
\(= -3 - 2√3\)
\(≒ -3 – 2*1.7 = -3 – 3.4 = -6.4\)
\(\{\frac{\sqrt{3}}{\sqrt{3}+2}\}+\{\frac{\sqrt{3}}{{\sqrt{3}-2}}\}\)
\(= \{0.4\} – \{-6.4\}\)
\(= 0 – (-6) = 6.\)
Therefore, D is the answer.
Answer: D
