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What is the remainder when dividing 221 by 3?

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What is the remainder when dividing 221 by 3? [#permalink]

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New post 09 Jul 2015, 10:36
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What is the remainder when dividing \(2^{21}\) by 3?

A. 4
B. 3
C. 2
D. 1
E. 0
[Reveal] Spoiler: OA

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Last edited by Bunuel on 09 Jul 2015, 10:37, edited 1 time in total.
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What is the remainder when dividing 221 by 3? [#permalink]

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New post 09 Jul 2015, 10:44
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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.

Answer: C.
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Re: What is the remainder when dividing 221 by 3? [#permalink]

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New post 09 Jul 2015, 10:44
reto wrote:
What is the remainder when dividing \(2^{21}\) by 3?

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



2/3--->Remainder 2
2*2/3--->R=1
2*2*2/3--->R=2
2*2*2*2/3--->R=1

So Odd powers of 2 have a remainder of 2 on being divided by 3 and Even powers of 2 have a remainder of 2 on being divided by 3.

Since 21 is an Odd power, the remainder should be 2.

Answer: C
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What is the remainder when dividing 221 by 3? [#permalink]

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New post 09 Jul 2015, 10:50
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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Re: What is the remainder when dividing 221 by 3? [#permalink]

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New post 02 Feb 2018, 07:30
reto wrote:
What is the remainder when dividing \(2^{21}\) by 3?

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

\(\frac{2^{21}}{3}\)

Or, \(\frac{2^{16}*2^5}{3}\)

\(2^{16}\) will leave a remainder of 1 when divided by 3
\(2^5\) will leave a remainder of 2 when divided by 3

Thus, the final remainder will be 2, answer will be (C)
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What is the remainder when dividing 221 by 3? [#permalink]

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New post 02 Feb 2018, 10:03
reto wrote:
What is the remainder when dividing \(2^{21}\) by 3?

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


exponent→ones unit cycle for 2:
2^1→2
2^2→4
2^3→8
2^4→6
thus, 2^21 gives a ones unit of 2
2/3 leaves a remainder of 2
C
What is the remainder when dividing 221 by 3?   [#permalink] 02 Feb 2018, 10:03
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