First slide

Permutations

Question

The number of ordered pairs $(m, n), m, n \in {1, 2 \dots, 50}$ such that $6^{m} + 9^{n}$ is a multiple of 5 is

Moderate

A

1250
B

2500
C

500
D

625

Solution

As the last digit of $6^{m}, m \in N$ is $6, 6^{m} + 9^{n}$ will be divisible by 5 if the unit’s digit of $9^{n}$ is 4 or 9. This is possible when n is odd.
$∴$ required number of ordered pairs $= 50 x 25 = 1250 .$

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