Question

# How many ordered pairs of (m, n) integers satisfy $$\displaystyle\frac{m}{12}=\frac{12}{n}$$?

A
30
B
15
C
12
D
10

Solution

## The correct option is B $$15$$$$m \times n = 144$$144 can be written in multiplication of two integers in the following ways:$$1 \times 144 = 2 \times 72 = 3 \times 48 = 4 \times 36 = 6 \times 24 = 8 \times 18 = 9 \times 16 = 12 \times 12$$For all the factors except $$(12, 12)$$ there would be 14 ordered pairs.Adding one more, yields 15 possibilitiesMathematics

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