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The product of two consecutive natural numbers is 72. Find the numbers.

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8 and 9

7 and 9

6 and 9

5 and 9

answer is A.

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Detailed Solution

Let x be the lesser number. The bigger integer is then x+1.
Their product is 72. Thus,

\Rightarrow x (x + 1) = 72

\Rightarrow x^{2} + x - 72 = 0

\Rightarrow x^{2} + 9 x - 8 x - 72 = 0

\Rightarrow x (x + 9) - 8 (x + 9) = 0

\Rightarrow (x - 8) (x + 9) = 0

\Rightarrow x = 8 or x = - 9

Due to the fact that the integers are natural numbers, thus, we neglect -9.
So,

x = 8

Therefore, 8 and 9 are the next two natural numbers.
Hence, option 1 is correct.

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