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CGP EDU Academic Team
Published on: August 14, 2026
'n' is selected from the set {1, 2, 3, ………. 100} and the number 2 n + 3 n + 5 n is formed. Total number of ways of selecting 'n' so that the formed number is divisible by 4, is equal to ……....
Text Solution
Verified by ExpertsThe correct answer is:
0049
Ans. 0049
Sol. If n is odd, then 3 n = 4 λ 1 – 1
5 n = 4 λ 2 + 1
2 n + 3 n + 5 n is divisible by four if n ≥ 49 i.e.
n can take 49 different values. If n is even then
3 n = 4 λ , 5 n = 4 λ 2 + 1
2 n + 3 n + 5 n is not divisible by 4 as 2 n + 3 n + 5 n will be in the form of 4 λ + 2.
Thus total number of ways of selecting 'n' = 49.
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