Is a non integer K divisible by 24?

Question

Is a non negative integer K divisible by 24?
A)K = x^3-x where x is an odd integer
B) K is divisible by both 12 and 2

Donnie84 · Answer

Hey stonecold, Isn't this task same as: if-k-is-a-positive-integer-what-is-the-remainder-when-224413.html

stonecold · Answer

Thanks i have edited the Question. You may try this one

Regards Stone Cold

Donnie84 · Answer

Hmm, not sure. Isn't statement 1 contradicting information given in the stem?
As per statement 1, k will be an integer.
Am I missing something?

stonecold · Answer

Non Negative

I need to type the questions myself This Copy paste thing isnt working

Donnie84 · Answer

Ok, let's see now.

St1:

k = x^3-x where x is an odd integer
 = x(x^2 - 1)
 = (x-1)(x)(x+1) -> k is the product of 3 consecutive integers.

If x = 1, k = 0 which is allowed as per information given in the stem. Non-negative includes 0. 0 is divisible by any integer.
If x = 3, k = 24 which is divisible by 24.
For all other odd integer values of x, k will always have at least one 24 in it.
Sufficient.

St2:

k is divisible by both 12 and 2.

If k= 12 -> not divisible by 24.
If k = 24 -> divisible by 24.
Insufficient.

Answer (A).

Is a non integer K divisible by 24?

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