Folks, again this is simple if u know the basic concepts of remainders.
Let's look at this simple problem first.
Remainder obtained when 11xK is divided by 4 is nothing but the remainder obtained when 11 is divided by 4 x K divided by 4
ie the remainder of 11xK / 4 will be of the form 3xK (in case 3xK is greater than 4 it will be further divided by 4 to get the remainder)
Similarly when 11xK + 17 is divided by 9 the remainder will of the form 2xK + 8.
Using this concept to the given problem
4+7n/3 the remainder will be of the form 1 + n. ( So the remainder now depends upon the value of n)
Statement 1: Since it is given that n+1 is divisible by 3.
Hence 4 + 7n / 3 the remainder will be 0.
So statement 1 alone is sufficient.
Statement 2: n > 20.
For different values of n we get different remainders.
So statement 2 is not sufficient
Cicerone, why are you taking 3 and 2? and not 2 and 1? Can you pls clarify?
when 11 is divided by 4 the reamainder is 3
So 11k divided by 4 the remainder will be of the form 3k
Similary 11 divided by 9 the remainder is 2
So 11k divided by 9 the remainder will be of the form 2k
Let me be more clear
Let's take 45. When 45 is divided by 8 the remainder is 5
Now 45 = 9 x 5
Now 9 leaves a remainder 1 when divided by 8
and 5 leaves a remainder 5 when divided by 5.
Since 45 = 9 x 5
The remainder also will be remainder of 9/8 x remainder of 5/8
ie 1 x 5 = 5
Let's take another example
2272/6 the raminder is 4
Now 2272 = 32 x 71
32/6 the remainder is 2
71/6 the remainder is 5
So according to our rule the remainder must be 2 x 5 = 10
Since 10 is greater than 6 it is further divided and hence the remainder becomes 4.
So all the three basic operations i.e additon, subtraction and multiplication of remainders can be done.
i.e Remainder of 45k + 23p - 17q when divided by 12 will take the form of 9k + 11p - 5q.
I think this is clear to everyone