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Asked by swayamagarwal2114 | 01 Aug, 2022, 01:47: AM
Expert Answer
When we change the value of x, the given expression [2x] + [4x]+ [6x] + [8x] changes only for rational values like p/q where q is divisible by the numbers 2, 4, 6, 8
So, we need to look for the numbers of the form p/lcm(2, 4, 6, 8) = p/24
For 1/24, 2/24, we get 0 such cases.
For 3/24, we get 1 case
FOr 4/24, 5/24, we get 2 cases
Similalrly, for the rest
Finally we get 12 out of first 20 integers.
So, total = 12 x 50 = 600
Thus, k is divisble by 100
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