First slide

Combinations

Question

$The number of ordered pairs (m, n) where m, n \in {1, 2, 3, \dots \dots 50} such that 6^{m} + 9^{n} is a multiple of 5 is$

Moderate

A

1250
B

2500
C

625
D

500

Solution

$Unit digit of 6^{m} is 6$
$∴ Unit digit of 9^{n} will be 9 or 1$
$For 6^{m} + 9^{n} t o divisible by 5 unit digit of 9^{n} must be 9$
$∴ n must be odd.$
$∴ Total number of ordered pair = 50 \times 25 = 1250$

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