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Question

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


A
30
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B
15
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C
12
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D
10
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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 possibilities

Mathematics

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