Question

The difference between two numbers is $1365$. When the larger is divided by the smaller, the quotient is $6$ and the remainder is $15$. What is the smaller number?

• A. $240$
• B. $360$
• C. $270$
• D. $295$

Hint:

For quotient–remainder problems, write $L = qs + r$ and plug into any extra condition (like sum or difference) to solve directly.

Answer 1

The Correct Option is C

Step 1: Set up Euclidean division.
Let the smaller number be $s$ and the larger be $L$.
“Quotient $6$, remainder $15$” ⇒ $L = 6s + 15$. Step 2: Use the difference condition.
$L - s = 1365 ⇒ (6s + 15) - s = 1365$
$⇒ 5s + 15 = 1365 ⇒ 5s = 1350 ⇒ s = 270$. \[ \boxed{270} \]