If the integers m and n are chosen at random out of integers 1 to 100, with replacement, then the probability that a number of the form (7m + 7n) is divisible by 5 equals.....

For 7(m+n) to be divisible by 5, (m+n) should be a multiple of 5 because 7 and 5 are coprime.
So, (m+n) = 5k
If k = 1, 4 values are possible
If k = 2, 9 values are possible and so on till k = 40, when 199 values are possible. Total number of cases = 4 + 9 + 14 + ... + 199 = 40/2 * (2*4 + 39*5) = 4060
Required probability = 4060/10000 = 0.406

shouldn't "k" be till 40?