Question

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

• A. 15 and 16
• B. 16 and 17
• C. 17 and 18
• D. 18 and 19

Answer 1

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 = $x\times (x+1)=306$
$\Rightarrow x^2+x=306$
$\Rightarrow x^2+x-306=0$
$\Rightarrow x^2+18x-17x-306=0$
$\Rightarrow x(x+18)-17(x+18)=0$
$\Rightarrow (x+18)(x-17)=0$
Either $x+18=0orx-17=0$
$\Rightarrow x=-18orx=17$
Since, it's given integers are positive $x$ can only be $17$
$\therefore x+1=17+1=18$
Therefore, two consecutive positive integers will be $17$ and $18$.