Question

If seven-digit number made up of all distinct digits $8,7,6,4,2,x$ and $y$ is divisble by $3$, then

• A. Maximum value of $x-y$ is $9$
• B. maximum value of $x+y$ is $12$
• C. $\sum (x+y)=60$
• D. minimum value of $x-y$ is $3$

Answer 1

Answer: (A), (B), (C)

$\sum (x+y)=60$

$8,7,6,4,2,x$ and $y$
Any number is divisible by $3,$ if sum of digits is divisible by $3.$

i.e,. $x+y+27$ is divisible by $3$
$\therefore x+y$ is divisible by $3$.

Possible pairs are $(5,1)(3,0)(9,0)(9,3)$ and $(1,5),(0,3)(0,9)(3,9)$
$\therefore \sum (x+y)=60$