If the symbol [x] denotes the greatest integer less than or equal to x, then the value of : $$\left[ {\frac{1}{4}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{1}{{50}}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{2}{{50}}} \right]$$ $$ + $$ $$....$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{{49}}{{50}}} \right]$$
Options:
A . 0
B . 9
C . 12
D . 49
Answer: Option C Clearly, each of the 38 terms $$\left[ {\frac{1}{4}} \right], \left[ {\frac{1}{4} + \frac{1}{{50}}} \right], \left[ {\frac{1}{4} + \frac{2}{{50}}} \right], $$ $$ ..... $$ $$ , \left[ {\frac{1}{4} + \frac{{37}}{{50}}} \right]$$ has a value lying between 0 and 1, While each one of the 12 terms $$\left( {\frac{1}{4} + \frac{{38}}{{50}}} \right),$$ $$\left( {\frac{1}{4} + \frac{{39}}{{50}}} \right),$$ $$.....,$$ $$\left( {\frac{1}{4} + \frac{{49}}{{50}}} \right)$$ has a value lying between 1 and 2. Hence, the given expression = (0 × 38) + (1 × 12) = 12
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