If the integer m and n are chosen at random between 1 and

Home » Aptitude » Probability » Question

If the integer m and n are chosen at random between 1 and 100, then the probability that a number of the from 7^m + 7ⁿ is divisible by 5 equals ?

1. 1/4
2. 1/7
3. 1/8
4. 1/49

Correct Option: C

Number of possible cases = 100 x 100 for 7^m + 7ⁿ to be divisible by 5,
One of the term has to end with 9 and other with 1 (7^m cannot be divided by 9 )

⇒ m can be 2, 6 , 10, 14, ..... 98 (25 values) and n can be 4, 8, 12 ...... 100(25 values)

Since m and n can interchange
∴ Required probability = (2 x 25 x 25) / (100 x 100) = 1/8