rapper wrote:For a nonnegative integer n, if the remainder is 1 when 2n is divided by 3, then which of

the following must be true?

I. n is greater than zero.

II. 3n = (-3)n

III. √2n is an integer.

A. I only

B. II only

C. I and II

D. I and III

E. II and III

Hi guys i got its answer as D.Is it correct?

Here we first see the multiples of 3 are 3,6,9,12,15,18,21,24.....so on

multiples of 2 are 2,4,6,8,10,12,14,16,18,20,22,24,26


We observe when the multiples of 2 are a perfect square like 4, 16, then the remainder is 1 when divided by 3 also , the third condition i.e √2n is an integer holds true.

√4= 2(integer)
√16=4(integer)
√64=8(integer)

Hence I and III condition hold true.

Answer is D

what about number 10 = 2 X5

this is not a perfect square ...

IMO - A

I would go with A on this one.

Because for option 3, it could be true in some cases and not true as well. Example - 10, 14 etc..

Yes you guys are right, seems like i missed some cases here. In fact this is called a blunder!

answer seems A here.