n is selected from the set {1, 2, 3, . . ., 100} and the number 2n + 3n + 5n is formed. Total number of ways of selecting n so that the formed number is divisible by 4 is equal to

If n is odd,      3n=4λ1−1,5n=4λ2+1⇒ 2n+3n+5n is divisible by 4 if n≥2Thus, n = 3,5,7,9, ...,99, i.e., n can take 49 different values.If n is even, 3n=4λ1+1,5n=4λ2+1⇒ 2n+3n+5n is not divisible by 4 as 2n+3n+5n will be in the form of 4λ+2. Thus, the total number of ways of selecting 'n' is equal to 49 .