What is the remainder

[shady320]

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

[RonPurewal]

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

(1)
multiply out (k+1)^3 = k^3 + 3(k^2) + 3k + 1.
all of these terms are multiples of k (which don't contribute to the remainder upon division by k) except for the last one, so the remainder must be 1.

(2)
there is no information about n, so this statement is insufficient.

so (a).

--

also note that you should be extremely reluctant to pick answer choice (c) on this problem -- that answer choice is a definite "trap answer". i.e., it's far too easy -- it actually gives you numerical values of the two variables -- and it doesn't make any use of the fact that the question itself is about remainders.
so, if you can eliminate statement 2 (which shouldn't be that hard) and then dismiss (c) as a trap answer, the only choice that's actually left at that point is the correct answer!

[sfbay]

remainder of 1

[mithunsam]

n/k = (k+1)^3 / K
= (k^3 + 1^3) / k
= k^2 + 1/k

remainder of 1

not sure if this would work for all remainders or just lucky cause it is 1 (1^3 = 1)

Not correct.

(k+1)^3 / K is not (k^3 + 1^3) / k. When you expand, you will get k^3 + 3(k^2) + 3k + 1.

[RonPurewal]

Not correct.

(k+1)^3 / K is not (k^3 + 1^3) / k. When you expand, you will get k^3 + 3(k^2) + 3k + 1.

yes, thanks.

also note that this result is in my post, directly above the incorrect post.

read the thread, people!

[gal.afgon]

Not correct.

(k+1)^3 / K is not (k^3 + 1^3) / k. When you expand, you will get k^3 + 3(k^2) + 3k + 1.

yes, thanks.

also note that this result is in my post, directly above the incorrect post.

read the thread, people!

I believe there is another great way :

(k+1)^3 is (k+1)(k+1)(k+1) . when you divide it by K each on of (k+1) has a reminder of 1 by that you can conclude that the reminder will be 1 because (1)(1)(1)/K is 1 {(1) - meant to be the reminder of each k+1 when divide by k}

[jlucero]

This does work in this instance, but two things:

1) This method wouldn't work for any other numbers other than k+1 and k. Ron's method could give you a way to see what the possible remainders are if this were (k+2)^3.

2) The way that you're multiplying all those remainders doesn't really work here. If you divided first and then multiplied the three answers with remainders, you'd get something that looked like this:
q = quotient
r = remainder
(q + r)(q + r)(q + r)

Note that you aren't just multiplying the remainders together... you're multiplying the remainders time each other and also against other quotients. You could solve this problem using this algebra, but, I'd recommend against it because the math is much trickier here.