Question

If the integers M and n are chosen from the numbers 1,2,3....100. independently, then the probability that 7^m + 7ⁿ is divisible by 5.

• A. ½
• B. ¼
• C. 1/8
• D. 1/16

Answer 1

Answer: (B)

¼

Answer 2

When 7^m is divided by 5 remainders will be 1,2,3,4

7m	7n
25 – 5k + 1	5p + 1 – 25
25 – 5k + 2	5p + 2 – 25
25 – 5k + 3	5p + 3 – 25
25 – 5k + 4	5p + 4 – 25

P(5) = $\frac { 1 } { 4 } \times \frac { 1 } { 4 } + \frac { 1 } { 4 } \times \frac { 1 } { 4 } + \frac { 1 } { 4 } \times \frac { 1 } { 4 } + \frac { 1 } { 4 } \times \frac { 1 } { 4 } = \frac { 1 } { 4 }$ .