Question

A whole number larger than $2$ leaves a remainder of $2$ when divided by each of the numbers $3, 4, 5,$ and $6.$ The smallest such number lies between which two numbers?

$40\ \text{and}\ 49$

$60 \text{ and}\ 79$

$100\ \text{and}\ 129$

$210\ \text{and}\ 249$

$320\ \text{and}\ 369$

Answer: B

Concepts:least common multiple modular arithmetic

Difficulty rating: 1220

Solution:

Let $x$ be the number. Then $x - 2$ is divisible by $3, 4, 5,$ and $6.$

The least common multiple of these numbers is $60,$ which makes $x$ $62.$

Thus, B is the correct answer.

2004 AMC 8 Problem 19

Answer: B

Difficulty rating: 1220

Solution:

Problem 19 in Other Years