If n is a positive integer, for which of the following would the units digit always be equal to the units digit of n?

I. n^5

II. n^10

III. n^25

Answer Choices

Correct answer marked below

I only

II only

III only

I and III only

Correct

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

Unlock the full explanation

Create a free account to reveal the correct answer, see the step-by-step explanation, and start tracking your GMAT progress.

Create free account Sign in

Comments

ChinenyeSep 29

Solid question. The people who just test n=1 and n=2 will pick E and feel great about it lol.

NaveenSep 30

facts. always test a digit that cycles weirdly, not just small easy ones

MohitaMay 23

Is the reason II fails that some units digits have a cycle length that isn't a factor of 10? Trying to make sure I'm not just memorizing.

BharathMay 31

yeah basically. the digits that behave badly have a cycle length that divides 4 but not 10, so raising to the 10th doesn't land you back where you started

What this question tests

What it tests

Your command of divisibility, primes, factors, parity, and how the GMAT tests properties of integers.

Common trap

Forgetting that 1 is not prime, that 0 is divisible by every integer, or that negative numbers flip your assumptions.

If n is a positive integer, for which of the following would the units digit always be equal to the units digit of n?I. n^5II. n^10III. n^25