Question

# The product of two consecutive positive integers is 306. Find the integers.

A

15 and 16

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B

16 and 17

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C

17 and 18

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D

18 and 19

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Solution

## The correct option is C 17 and 18 Let the first integer number = x Next consecutive positive integer will = x+1 Product of both integers = x×(x+1)=306 ⇒x2+x=306 ⇒x2+x−306=0 ⇒x2+18x−17x−306=0 ⇒x(x+18)−17(x+18)=0 ⇒(x+18)(x−17)=0 Either x+18=0 or x−17=0 ⇒x=−18 or x=17 Since, it's given integers are positive x can only be 17 ∴x+1=17+1=18 Therefore, two consecutive positive integers will be 17 and 18.

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