If P = k^3 - k^2, where k and P are positive integers, is P divisible

Rabab36 - Not sure if this was a question for me, or if you intended to present your version of the solution.

However, as you quoted my response , responding to the above quoted question

From the question stem we know

\(P = k^3 - k^2\)

If we take \(k^2\) common

\(P = k^2(k -1)\)

In a scenario when k is odd, for P to be divisible by 4, (k - 1) should be divisible by 4. This is because k is odd, so \(k^2\) will not be divisible by 4.

Ex. k = 5

P = \(5^2(5-1)\)

We can tell P is divisible by 4, as (5-1) is divisible by 4.

The inference does not intend to conclude that whenever k is odd, k - 1 is divisible by 4. I guess you inferred this from the statements in blue.

The inference is in conjunction with the question, "Is P divisible by 4". So if P were to be divisible by 4, and k was odd, then (k-1) would be divisible by 4.

Hope this clarifies.

then sir for x=5 n=3

statement is insufficient

K-1 is not necessarily divisible by 4 for odd value of k, which is why statement 1 is insufficient. Could someone pls explain why A is correct ?

Hey buddy just calculate the value of K^2(K-1) and divide it by four you’ll get the answer

For statement 2 we just that K^2(K-1) is even which tell us nothing whether that even number is a multiple of 4 or not

so 1 alone is sufficient!

Hello gmatophobia In S1 "It's given that x & n > 1, so k-1 will always be an even integer which is divisible by 4.", how did you arrive at x>1? further, even if both x & n are >1, lets say x=3 and n=5, k = 775, then k-1=774 which although is even but not divisible by 4. Bunuel , chetan2u , any other expert please clarify

Hi

There is no reason for statement 1 to be sufficient.
Is P divisible by 4 means is k^2(k-1) divisible by 4.

Statement 1 tells us that k is odd, so the question now becomes- Is k-1 divisible by 4?
There is nothing in statement that can give a YES or NO to the question.