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# If x=(999^99)×(899^100), what is the units digit of x?

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If x=(999^99)×(899^100), what is the units digit of x?  [#permalink]

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18 Apr 2016, 01:15
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84% (00:33) correct 16% (01:03) wrong based on 91 sessions

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If $$x=(999^{99})×(899^{100})$$, what is the units digit of x?

A. 0
B. 1
C. 3
D. 8
E. 9

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Joined: 19 Jan 2016
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Re: If x=(999^99)×(899^100), what is the units digit of x?  [#permalink]

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18 Apr 2016, 05:18
9 has a cyclicity of 2 (9,1)

For odd power, the unit digit is 9 and 1 for even power. so, 1*9 = 9.
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If x=(999^99)×(899^100), what is the units digit of x?  [#permalink]

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18 Apr 2016, 07:15
There are two cycles for 9
9^1 = 9
9^2 = 1
9^3 = 9
etc...

So 9 to an odd power times 9 to an even power means that it will be 9*1, giving a 9 as answer.
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If x=(999^99)×(899^100), what is the units digit of x?  [#permalink]

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18 Apr 2016, 08:25
Bunuel wrote:
If $$x=(999^{99})×(899^{100})$$, what is the units digit of x?

A. 0
B. 1
C. 3
D. 8
E. 9

$$9^{odd}$$= Units digit 9

$$9^{even}$$ = Units digit 1

Here we have $$9^{odd}$$ x $$9^{evevn}$$ => 9 x 1 =9

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Re: If x=(999^99)×(899^100), what is the units digit of x?  [#permalink]

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14 May 2017, 19:42
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