Question

Digits of 3-digit $A$ reversed to make $B$. If $B>A$ and $B-A$ divisible by 7, then:

• A. $100<A<299$
• B. $106<A<305$
• C. $112<A<311$
• D. $118<A<317$

Hint:

Write numbers in digit form and apply divisibility conditions.

Answer 1

The Correct Option is C

$B-A = 99(t-u)$ divisible by 7 ⇒ $t-u$ multiple of 7 ⇒ $t-u=7$ or $14$. Given $B>A$, $t>u$. Considering 3-digit constraints yields range $112<A<311$. \[ \boxed{112<A<311} \]