Consider a positive integer Y that, when divided by 9, leaves a remainder of 4. Which of the following statements must be true?
I. Y is even
II. Y cannot be a prime number
III. (Y + 5) divided by 9 has a remainder of 0.

Answer Choices

Correct answer marked below

I only

I and II only

III only

Correct

I and III only

I, II and III

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Explanation

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Official Explanation

Official

We analyze the statements based on the condition that Y divided by 9 gives a remainder of 4. Statement I: Not True. For example, 13 divided by 9 gives a remainder of 4, and 13 is odd. Statement II: Not True.…

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Comments

AmritApr 7, 2025

good question

WongMar 10, 2025

Good question

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.

Consider a positive integer Y that, when divided by 9, leaves a remainder of 4. Which of the following statements must be true? I. Y is even II. Y cannot be a prime number III. (Y + 5) divided by 9 has a remainder of 0.