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

(1) n is multiple of 5. If n=5, then n yields the remainder of 5 when divided by 6 but if n=10, then n yields the remainder of 4 when divided by 6. We already have two different answers, which means that this statement is not sufficient.

(2) n is a multiple of 12. Every multiple of 12 is also a multiple of 6, thus n divided by 6 yields the remainder of 0. Sufficient.

Answer: B.

Hope it's clear.
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Thanks a lot for the resources! Will do!

(1).

N=5A N can be 5,10,15,20,25 .... Now these values have different remainders when divided by 6 hence Insufficient

(2).

N= 12B = > N => 6 (2B) = > N = 6C .... Hence Remainder when N is divided by '6' is '0' => Sufficient

Hence (B) !!

I need some clarification on the first statement...

I know the numbers go like this: 3, 9, 15.....

But when 3 is divided by 6...how is that a remainder of 3?

THEORY:
Positive integer \(a\) divided by positive integer \(d\) yields a reminder of \(r\) can always be expressed as \(a=qd+r\), where \(q\) is called a quotient and \(r\) is called a remainder, note here that \(0\leq{r}<d\) (remainder is non-negative integer and always less than divisor).

For example positive integer n is divided by 25 yields the remainder of 13 can be expressed as: \(n=25q+13\). Now, the lowest value of \(q\) can be zero and in this case \(n=13\) --> 13 divided by 25 yields the remainder of 13. Generally when divisor (25 in our case) is more than dividend (13 in our case) then the reminder equals to the dividend. For example:
3 divided by 24 yields a reminder of 3 --> \(3=0*24+3\);
or:
5 divided by 6 yields a reminder of 5 --> \(5=0*6+5\),
or example from your post:
2 divided by 5 yields a reminder of 2 --> \(2=0*5+2\).

Hope it's clear.
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take 5 and 10 as n and we can can easily discard statement 1
Now as per statement 2 => N=12p => 6x => remainder will be zero
hence B
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Statement 1:
Options for n = 5, 10, 15, 20...
When 10 is divided by 6, the remainder is 4.
When 15 is divided by 6, the remainder is 3.
Since the remainder can be different values, INSUFFICIENT.

Statement 2:
Options for n = 12, 24, 36, 48...
When 12 is divided by 6, the remainder is 0.
When 24 is divided by 6, the remainder is 0.
When 36 is divided by 6, the remainder is is 0.
Since the remainder is the same in every case, SUFFICIENT.

The correct answer is B.
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Target question: What is the remainder when the positive integer n is divided by 6?

Statement 1: n is multiple of 5
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 10. In this case, the answer to the target question is the remainder is 4 when n is divided by 6
Case b: n = 15. In this case, the answer to the target question is the remainder is 3 when n is divided by 6
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n is a multiple of 12
If n is a multiple of 12, then we can write: n = 12k for some integer k
If n = 12k, we can also write: n = (6)(2)k, which tells us n is a multiple of 6
If n is a multiple of 6, then n divided by 6 will leave remainder 0
So, the answer to the target question is the remainder is 0 when n is divided by 6
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
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(1) \(n= 5 \ the \ remainder \ is \ (\frac{5}{6}) =5\)

\(n= 10 \ the \ remainder \ is \ (\frac{10}{6})=4 \) Insufficient

(2) \(n \ can \ be \ 12, 24, 36... \ divided \ 6 \ remainder \ is \ 0\). Sufficient.

The answer is B
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