Question

State true or false:

Two consecutive even natural numbers whose product is $168$ are $12$ and $14$.

• A. True
• B. False

Answer 1

The correct option is A True

Let the two consecutive even natural numbers be $a$ and $b$
Difference of two even numbers would always be even.

$\therefore a-b=2$

$a=b+2$.........(1)
$ab=168$
Hence, $(b+2)b=168$........... From (1)
$b^2+2b-168=0$
$b^2+14b-12b-168=0$
$(b+14)(b-12)=0$
$b=-14$ or $12$. Since, the numbers are positive hence $b=12$ and $a=b+2=12+2=14$