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# What is the units digit of 2^99?

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Math Expert
Joined: 02 Sep 2009
Posts: 53066
What is the units digit of 2^99?  [#permalink]

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29 Mar 2018, 22:42
00:00

Difficulty:

15% (low)

Question Stats:

89% (00:45) correct 11% (00:56) wrong based on 62 sessions

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What is the units digit of 2^99?

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

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Joined: 05 Mar 2018
Posts: 3
Re: What is the units digit of 2^99?  [#permalink]

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29 Mar 2018, 22:51
e) 8 . 99:4, remainder 3

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Re: What is the units digit of 2^99?  [#permalink]

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29 Mar 2018, 22:53
unit digit of any number is always the remainder of 10 when that number is divided by 10.
Remainder
2/10=2
2^2/10=4(by remainder theorem)
2^3/10=8(by remainder theorem)
2^4/10=6(by remainder theorem)
Now it will start repeating in grp of 4. So 99/4 remainder will be 3. so
remainder will be same as 2^3/10=8
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Re: What is the units digit of 2^99?  [#permalink]

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29 Mar 2018, 22:59
Principle to calculate remainder.
1) divide the exponent by 4, and find remainder.
2) unit digit of expression will be the unit digit of base raised to power of remainder.
If remainder is 0. Raise to power of 4.

Here the remainder 99/4 is 3
So answer will be unit digit of 2^3= 8

E

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Re: What is the units digit of 2^99?  [#permalink]

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29 Mar 2018, 23:01
Bunuel wrote:
What is the units digit of 2^99?

(A) 0
(B) 2
(C) 4
(D) 6
(E) 8

2 has a cyclicity of 4 = 2 , 4 , 8 , 6

We have 99/4 = 24 rem 3

Therefore units digits of 2^99 will be the same as units digit of 2^3 = 8

(E)
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Re: What is the units digit of 2^99?  [#permalink]

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29 Mar 2018, 23:08
ans should be D
Unit digits of the powers of two
2^1=2
2^2=4
2^3=8
2^4=6
2^5=2...... and follows the same trend as above

So, 2^99=6 as unit digit
Re: What is the units digit of 2^99?   [#permalink] 29 Mar 2018, 23:08
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