When 10 is divided by the positive integer $n$ , the remainder is $n - 4$ . Which of the following could be the value of $n$ ?

Correct answer marked below

3

4

7

Correct

8

12

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Comments

LinnJun 15

Wait, the remainder is n - 4? So if n = 7, remainder is 3. That works since 10 = 1*7 + 3. Is that the logic?

BookJun 24

But careful, remainder has to be less than the divisor too.

RenanAug 30

This one took me a second. The remainder being n - 4 is so weirdly worded. I kept trying to set up 10 = qn + (n-4).

JohnSep 3

Same here. Once you realize you can just test the choices it's way faster.

ArzishJul 19

Testing n = 3 gives remainder of -1, which is impossible, right? So that rules out A.

Fluffy4d ago

Pretty straightforward but I like how it sneaks in the constraint that remainder must be non-negative. Good reminder to always check that.

Aagreetjust now

Also remainder must be less than n, which n-4 is only when n > 4.

What this question tests

Your understanding of divisibility rules, least common multiples, and greatest common factors.

Forgetting that 1 is not prime and that every integer divides 0.

When 10 is divided by the positive integer nnn, the remainder is n−4n - 4n−4. Which of the following could be the value of nnn?