What is the remainder when the positive integer n is divided

Question

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
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient

rashminet84 · Answer

Ans should be A

You can pick numbers for K and N that satisfy sttmt 1 and check, everytime remainder will come as 1.

You can also use a principle that says -

if N/k gives remainder = x

then aN/k will give remainder ax (as long as ax < k)

if N was k+1, remainder would be 1 always
but if N = (k+1)^3, remainder will be 1^3

B is not sufficient.

pmal04 · Answer

if N = (k+1)^3, remainder will be 1^3--can you please explain this stm in detail?

maliyeci · Answer

(k+1)^3=k^3+3k^2+3k+1. So the remainder is always 1

rashminet84 · Answer

There is a remainder theorem that states

If x/y gives remainder z

then ax/y will give remainder az, as long as az is < y

in addition

if p/y gives remainder q

then p*x/y will give remainder z*q........ as long as zq is < y

N = (k+1)^3

K+1/k will always give remainder of 1

so when (k+1)(k+1)(K+1) is divided by K, i will give remainder of 1*1*1.....ie 1

But we have to be carefull while using this theorem, its safe as long as remainder is 1, otherwise care has to be taken that the remainder doesn't exceed the divisor, because in that case, the rule cannot be applied.

vannu · Answer

Answer is A
Stat 1

plug in numbers

n = (k+1)^3

Let K be 2
n=(2+1)^3
n=3^3 =9
n/k=9/2 ---the remainder is 1

n = (k+1)^3

Let K be 3
n=(3+1)^3
n=4^3 =64
n/k=64/3 ---the remainder is 1

n = (k+1)^3

Let K be 4
n=(4+1)^3
n=5^3 =125
n/k=125/4 ---the remainder is 1

A is suff

stat 2.
k = 5
we don't know about n..hence not suff.

vannu · Answer

I liked the tip.
Thanks!

What is the remainder when the positive integer n is divided

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