Question

The number of ordered pairs $(a,b)$ of positive integers, such that $a+b=90$ and their greatest common division is $6$, equals

• A. $5$
• B. $4$
• C. $14$
• D. $10$

Answer 1

The correct option is C $14$

Let's look at products of $6$
$6,12,18,24,30,36,42,48,54,60,66,72,78,84,90$
The pairs whose sums equal to $90$ are:
$6+84=90$
$12+78=90$
$18+72=90$
$66+24=90$
$60+30=90$
$54+36=90$
$48+42=90$
Total number of pairs are $7$.
But there can be $7$ more pairs when the numbers are reversed.
$\therefore$ total number of ordered pair are $14$