Pick the odd one out: 214, 350, 520, 738

I am preparing for an exam(NTSE), and I came across this puzzle(aptitude) in one of the quizzes. book(study guide NTSE). The book's author is Arihant Experts.

The question is to Pick the 'odd one out' and there are four options given.

214, 350, 520, 738.

The correct answer is 214. Can somebody explain why that is?

• You said this was in a book. What's the name of the book? What's the title of the quiz? If I wanted to look up this question myself, provide the information I would need to find it. See also How to reference material written by others: "For non-web-based citations, include the source to the best of your ability (title, author, page number, etc)." In other words, like I said, provide as much attribution information as you have available to you.
– Rubio
May 31, 2023 at 17:45
• @Rubio made changes as suggested.
– Max
May 31, 2023 at 17:57
• Thanks. You're going to want to add the same type of attribution to your other question before it gets closed for failure to attribute.
– Rubio
May 31, 2023 at 18:30

350 - because it is the only number with an even digit sum.

Or it could be:

738 - because it's the only multiple of 3

Or any number of other possibilities.

But I think the most likely reason for the given answer is:

All the others are of the form n^3+n.

350 = 7^3 + 7
520 = 8^3 + 8
738 = 9^3 + 9

And 214 is just shy of 222 = 6^3 + 6

• Nice catch. You must be really smart IRL.
– Max
May 31, 2023 at 21:27

214 is the only choice below 300.

What, that's not good enough?

Oh, ok - more than likely it's the odd choice because it's the only number given that has only two factors, 2 and 107. The other choices all have factors besides 2 and (n/2). That's pretty flimsy, but there's not much else here to go on.