Question

The smallest positive integer greater than 1 that leaves a remainder of 1 when divided by 4, 5, and 6 lies between which of the following pairs of numbers?

$2$ and $19$

$20$ and $39$

$40$ and $59$

$60$ and $79$

$80$ and $124$

Answer: D

Concepts:least common multiple modular arithmetic

Difficulty rating: 1020

Video solution:

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Written solution:

If a number leaves a remainder of $1$ when divided by $4,$ $5,$ and $6,$ then it is one more than the least common multiple of these numbers. The least common multiple is $60,$ so the smallest such positive integer is $60 + 1 = 61.$

Thus, D is the correct answer.

2017 AMC 8 Problem 12

Answer: D

Difficulty rating: 1020

Video solution:

Written solution:

Problem 12 in Other Years