When choosing an integer m randomly from 1 to 80, what is the probability that the product m(m+1) is divisible by 4?

Answer Choices

Correct answer marked below

1/4

1/3

1/2

Correct

2/3

3/4

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Explanation

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Official Explanation

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To determine the probability that the product m(m+1) is divisible by 4, we first note that m and m+1 are consecutive integers. Among any two consecutive integers, one of them is even. For the product m(m+1) to be divisible by 4, at least one of these integers must be divisible by 2 twice (i.e., one of them must be divisible by 4). The…

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Comments

AkilMar 26, 2025

Great question!

NaomiJun 30, 2024

cheers!

JayaNov 4, 2024

thank you taking time to upload it!

What this question tests

What it tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Common trap

Forgetting that 1 is not prime and that every integer divides 0.