Target question: What is the remainder when the positive integer "n" is divided by the positive integer "k"parinita wrote:What is the remainder when the positive integer "n" is divided by the positive integer "k" where k>1
(1) n = (k+1)^3
(2) k = 5
Statement 1: n = (k+1)^3
Now that we know the value of n, we can rewrite the target question as "What is the remainder when (k+1)^3 is divided by k?"
Let's expand and simplify (k+1)^3 to get . . .
(k+1)^3 =(k+1)(k+1)(k+1)
= (k+1)(k^2 + 2k + 1)
= k^3 + 3k^2 + 3k + 1
= k(k^2 + 3k + 3) + 1
So, we can now ask, "What is the remainder when k(k^2 + 3k + 3) + 1 is divided by k?"
As you can see, k(k^2 + 3k + 3) divided by k leaves remainder zero.
So, k(k^2 + 3k + 3) + 1 divided by k must leave remainder 1.
Since we can answer the rephrased target question with certainty, statement 1 is SUFFICIENT
Statement 2: k = 5
No information about n, so statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
