Given that x, y, and z are positive integers, and $24x = 36y = 60z$ , which of the following must be divisible by 3?

I. x
II. y
III. z

Answer Choices

Correct answer marked below

I only

II only

III only

I and III only

Correct

I, II and III

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Explanation

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Official Explanation

Official

To solve for the divisibility by 3, we start with the equations 24x = 36y = 60z. We can express each variable in terms of a common variable k: x = k/24, y = k/36, z = k/60. The least common multiple (LCM) of 24, 36, and 60 is 360. Thus, we can set k =…

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Comments

ZaberApr 12, 2025

Thankss

CharminglyOct 9, 2024

thanks

BriannaSep 18, 2024

thanks for posting

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.

Given that x, y, and z are positive integers, and 24x=36y=60z24x = 36y = 60z24x=36y=60z, which of the following must be divisible by 3? I. x II. y III. z