If the symbol [x] denotes the greatest integer less than or equal to x, then the value of :
$$\left[ {\frac{1}{4}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{1}{{50}}} \right]$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{2}{{50}}} \right]$$ $$ + $$ $$....$$ $$ + $$ $$\left[ {\frac{1}{4} + \frac{{49}}{{50}}} \right]$$
A. 0
B. 9
C. 12
D. 49
Answer: Option C
Solution(By Examveda Team)
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
Related Questions on Number System
Three numbers are in ratio 1 : 2 : 3 and HCF is 12. The numbers are:
A. 12, 24, 36
B. 11, 22, 33
C. 12, 24, 32
D. 5, 10, 15
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