First slide

Combinations

Question

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

Moderate

A

6250
B

1250
C

1875
D

None of these

Solution

All the numbers of the form 6ⁿ will end with 6 and 9^m will end with 9, if m is odd and will end with 1, if m is even. Therefore, 6ⁿ + 9^m will end with 5 if n is any number and m is odd.
Thus, number of ordered pairs = 50 × 25 = 1250.

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