| \[\frac{5-\left[ \frac{3}{4}+\left\{ 2\frac{1}{2}-\left[ \frac{1}{2}+\overline{\frac{1}{6}-\frac{1}{7}} \right] \right\} \right]}{2}\] is equal to |
A) \[1\frac{23}{168}\]
B) \[2\frac{23}{168}\]
C) \[3\frac{23}{168}\]
D) \[4\frac{23}{168}\]
E) None of these
Correct Answer: A
Solution :
| \[?=\frac{5-\left[ \frac{3}{4}+\left\{ \frac{5}{2}-\left( \frac{1}{2}+\overline{\frac{1}{6}-\frac{1}{7}} \right) \right\} \right]}{2}\] |
| \[=\frac{5-\left[ \frac{3}{4}+\left\{ \frac{5}{2}-\left( \frac{1}{2}+\frac{7-6}{42} \right) \right\} \right]}{2}\] |
| \[=\frac{5-\left[ \frac{3}{4}+\left\{ \frac{5}{2}-\left( \frac{1}{2}+\frac{1}{42} \right) \right\} \right]}{2}\] |
| \[=\frac{5-\left[ \frac{3}{4}+\left\{ \frac{5}{2}-\left( \frac{21+1}{42} \right) \right\} \right]}{2}\] |
| \[=\frac{5-\left[ \frac{3}{4}+\left\{ \frac{5}{2}-\frac{22}{42} \right\} \right]}{2}\] |
| \[=\frac{5-\left[ \frac{3}{4}+\left\{ \frac{105-22}{42} \right\} \right]}{2}=\frac{5-\left[ \frac{3}{4}+\frac{83}{42} \right]}{2}\] |
| \[=\frac{5-\left[ \frac{63+166}{84} \right]}{2}=\frac{5-\frac{229}{84}}{2}\] |
| \[=\frac{\frac{420-229}{84}}{2}=\frac{\frac{191}{84}}{2}=\frac{191}{84\times 2}\] |
| \[=\frac{191}{168}=1\frac{23}{168}\] |
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