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What is the remainder when dividing 221 by 3?
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09 Jul 2015, 11:44

reto wrote:

What is the remainder when dividing \(2^{21}\) by 3?

A. 4 B. 3 C. 2 D. 1 E. 0

This cannot possibly be a GMAT question. When dividing by 3 we can have only 3 remainders: 0, 1, or 2. 0 is clearly out, 2 in any integer power cannot be a multiple of 3. So, we are left with 1 or 2. Then, simple testing will tell us that 2 in odd powers gives the remainder of 2 while 2 in even powers gives the remainder of 1 when dividing by 3.

What is the remainder when dividing 221 by 3?
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09 Jul 2015, 11:50

reto wrote:

What is the remainder when dividing \(2^{21}\) by 3?

A. 4 B. 3 C. 2 D. 1 E. 0

2 when divided by 3 leaves remainder = 2 [i.e. 2 is in excess of 2 to be a multiple of 3]

which in other words can also be written as

2 when divided by 3 leaves remainder = -1 [i.e. 2 is short of 1 to be a multiple of 3]

i.e when \(2^{21}\) is divided by 3 the remainder will be \((-1)^{21} = -1 i.e. 2\)

Answer: Option C

Please Note: remainders can be written in Positive as well as in Negative form

e.g. When 11 is divided by 7 remainder is 4 or remainder is (-3) i.e. 11 has either excess of 4 or it is short by 3 to be a multiple of 7

e.g. When 39 is divided by 12 remainder is 3 or remainder is (-9) i.e. 39 has either excess of 3 or it is short by 9 to be a multiple of 12 _________________

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