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)
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >