Consider a positive integer Y that, when divi… | GMAT Sprint

Free Practice Question

PS · Problem Solving

sub-505

Divisibility/Multiples/Factors

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

See the full step-by-step explanation

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Track your performance and improve

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Start for free Sign in

Explanation

Preview

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.…

Read the full explanation

Create free account Sign in

Comments

AmritApr 7, 2025

good question

WongMar 10, 2025

Good question

YashApr 29

thanks, helpful explanation. the 'must be true' wording is what got me — I kept picking numbers that made I true by accident lol

SatvikMay 2

same here! I tried Y=4 first and thought 'oh its even' but then Y=13 broke it. classic trap.

AbderrahmenJul 16

this one felt pretty easy honestly, sub-505 makes sense. III is straightforward once you realize you just add the remainders

TanishAug 4

tiny tip for these remainder questions: write Y = 9k + 4 right away. it makes all three statements super quick to check.

WeeAug 12

this is the way. saved me so much time on test day

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.