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Please explain how to solve ques no. 4. The answer given is 8.

Please explain how to solve ques no. 4. The answer given is 8.

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Grade:12

2 Answers

Anish Singhal
askIITians Faculty 1192 Points
5 years ago
If the expression on LHS is greatest integer then it is not possible
jagdish singh singh
173 Points
5 years ago
\hspace{-0.75 cm}$ Given $\lfloor \frac{x}{3}\rfloor +\lfloor \frac{x}{4}\rfloor+\lfloor \frac{x}{6}\rfloor =\frac{3x}{4}$\\\\ So $\frac{x}{3}-\lfloor \frac{x}{3}\rfloor+\frac{x}{4}-\lfloor \frac{x}{4}\rfloor+\frac{x}{6}-\lfloor \frac{x}{6}\rfloor =0$\\\\ So $\{\frac{x}{3}\}+\{\frac{x}{4}\}+\{\frac{x}{6}\}=0\cdots (1)$\\\\ Given $x\in \{1,2,3,4,5,\cdots ,100\}$\\\\ So equation $(1)$ is true when $x\in 6n,1\leq n\leq 100$\\\\ So Total $8$ values of $x.$
 
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