ds - remainder

[ccassel]

How would you explain the answer to this question?

What is the remainder when the positive integer n is divided by 6?

(1) n is a multiple of 5
(2) n is a multiple of 12


cheers,

[Ian Stewart]

How would you explain the answer to this question?

What is the remainder when the positive integer n is divided by 6?

(1) n is a multiple of 5
(2) n is a multiple of 12


cheers,

The most useful strategy in most DS remainders questions is to simply find two or three examples of numbers that 'work'. For Statement 1, we know that n is a multiple of 5. Let's come up with two or three examples of n, and see if we always get the same answer to the question. n could be 10, in which case the remainder is 4 when n is divided by six, or n could be 15, in which case the remainder is 3 when n is divided by six. We can get two different answers to the question, so Statement 1 is not sufficient.

Now, for Statement 2, you could again come up with different values for n: 12, 24, 36, etc. In each case, the remainder is 0 when you divide by 6, which is persuasive evidence that Statement 2 is sufficient. Of course, any number that is a multiple of 12 must be a multiple of 6, which is the reason we always get a remainder of zero when we divide a multiple of 12 by six, but even if you don't see that, coming up with a few sample values for n can lead you to the right answer.

[MAAJ]

What is the remainder when the positive integer n is divided by 6?

Rephrase to: whats the remainder when divided by 2*3?

(1) n is a multiple of 5

n -> has 5,...? in its prime factors. So we know that its unit digit should be 0 or 5. But still not sufficient.

(2) n is a multiple of 12

n -> has 2,2,3...? in its prime factors. So it sure has 2*3 in its prime factors, hence it must be divisible by 6. If it's divisible by 6 then the remainder must be zero (0)

Correct Answer [spoiler](B)[/spoiler]

[ccassel]

Those are 2 good ways to answer the question.

Thanks,