monirjewel wrote:

For a nonnegative integer n, if the remainder is 1 when 2^n is divided by 3, then which of the following must be true?

I. n is greater than zero.

II. 3^n = (-3)^n

III. √2^n is an integer.

A. I only

B. II only

C. I and II

D. I and III

E. II and III

n is nonnegative integer - Immediately think of n = 0

When 2^0 = 1 is divided by 3, remainder is 1.

When n = 1, 2^1 divided by 3 gives remainder 2.

When n = 2, 2^2 = 4 divided by 3 gives remainder 1.

When a number is divided by 3, the remainder must be 0/1/2.

So here is the pattern: 2^n divided by 3 will not give 0 as remainder since 2^n has no 3s in it.

2^n will give remainder 1 when n is even.

2^n will give remainder 2 when n is odd.

Since we want the remainder to be 1, n MUST be even.

I. n is greater than zero.

Not necessary since n can be 0.

II. 3^n = (-3)^n

Since n is even, this must be true.

III. √2^n is an integer.

n is 0/2/4/... - In each case, this will be an integer.

Answer (E)

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Karishma

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