Max@Math Revolution wrote:What is the reminder when k^2 is divided by 8?

1) When k is divided by 2, the reminder is 1.
2) When k is divided by 3, the reminder is 2.


* A solution will be posted in two days.

Question :Remainder when k^2 is divided by 8?

Statement 1: When k is divided by 2, the reminder is 1
i.e. k is odd
i.e. k may be 1, 3, 5, 7, 9, ... etc
i.e. k^2 may be 1, 9, 25, 49, 81, ... etc
But Remainders when k^2 is divided by 8 may be only 1 (Consistent)
SUFFICIENT

Statement 2:When k is divided by 3, the reminder is 2.
i.e. k may be 5, 8, 11, ... etc
i.e. k^2 may be 25, 64, 121 ... etc
But Remainders when k^2 is divided by 8 may be only 1, 0, 1,... (Inconsistent)
NOT SUFFICIENT

Answer: Option A

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

What is the reminder when k^2 is divided by 8?

1) When k is divided by 2, the reminder is 1.
2) When k is divided by 3, the reminder is 2.


-> In the original condition, there is 1 variable(k), which should match with the number of equations. So you need 1 equation, which is likely to make D the answer.
For 1), k=2p+1=1,3,5,7... and n^2=1,9,25,49,... the remainder divided by 8 is 1, which is unique and sufficient.
For 2), in k=3n+2=2, 5, the remainders derived by dividing k2=4,25 with 8 are 4 and 1, which is not unique and not sufficient. Therefore, the answer is A.