Question

Let there be three natural numbers, if the product of first two natural numbers is $442$ and the product of last two natural numbers is $782$, then the sum of all three numbers is/are

• A. $70$
• B. $89$
• C. $234$
• D. $614$

Answer 1

Answer: (A), (B), (D)

The correct options are
A $70$
B $89$
D $614$

$442=1\times 2\times 13\times 17$
$782=1\times 2\times 17\times 23$
Middle number can be $1,2,17$ or $34$

If the middle number is $1$
Then the numbers will be $442,1,782.$
Sum of all numbers $=442+1+782=1225$

If the middle number is $2$
Then the numbers will be $221,2,391.$
Sum of all numbers $=221+2+391=614$

If the middle number is $17$
Then the numbers will be $26,17,46.$
Sum of all numbers $=26+17+46=89$

If the middle number is $34$
Then the numbers will be $13,34,23.$
Sum of all numbers $=13+34+23=70$

Hence, the possible sum are $1225,614,89$ or $70$