Question

If the integers \( m \) and \( n \) are chosen at random from 1 to 100, then the probability that a number of the form \( 7m + 7n \) is divisible by 5, equals to?

• A. \( \frac{1}{4} \)
• B. \( \frac{1}{8} \)
• C. \( \frac{1}{16} \)
• D. \( \frac{1}{5} \)

Hint:

The probability of divisibility by a number can be calculated by considering how often the sum of the terms is divisible by that number.

Answer 1

The Correct Option is A

The number \( 7m + 7n \) is divisible by 5 if the sum \( m + n \) is divisible by 5. Since both \( m \) and \( n \) are chosen randomly, the probability of this happening is \( \frac{1}{4} \).