| Simplify \[\frac{\left[ 3\frac{1}{4}\div \left\{ 1\frac{1}{4}-0.5\left( 2\frac{1}{2}-\overline{\frac{1}{4}-\frac{1}{6}} \right) \right\} \right]}{4\times \frac{1}{12}}.\] |
A) 245
B) 233
C) 234
D) 299
E) None of these
Correct Answer: C
Solution :
| \[\frac{\left[ 3\frac{1}{4}\div \left\{ 1\frac{1}{4}-0.05\left( 2\frac{1}{2}-\overline{\frac{1}{4}-\frac{1}{6}} \right) \right\} \right]}{4\times \frac{1}{12}}\] |
| \[=\frac{\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\left( \frac{5}{2}-\frac{3-2}{12} \right) \right\} \right]}{4\times \frac{1}{12}}\] |
| \[=\frac{\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\left( \frac{5}{2}-\frac{1}{12} \right) \right\} \right]}{\frac{1}{3}}\] |
| \[=\frac{\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{1}{2}\left( \frac{30-1}{12} \right) \right\} \right]}{\frac{1}{3}}=\frac{\left[ \frac{13}{4}\div \left\{ \frac{5}{4}-\frac{29}{24} \right\} \right]}{\frac{1}{3}}\] \[=\frac{\left[ \frac{13}{4}\div \left\{ \frac{30-29}{24} \right\} \right]}{\frac{1}{3}}=\frac{\left[ \frac{13}{4}\div \frac{1}{24} \right]}{\frac{1}{3}}\] |
| \[=\frac{13}{4}\times 24\times 3=13\times 18=234\] |
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