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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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New post 18 Apr 2016, 00:15
1
5
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (00:51) correct 20% (01:14) wrong based on 91 sessions

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

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New post 18 Apr 2016, 04:18
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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New post 18 Apr 2016, 06:15
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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New post 18 Apr 2016, 07:25
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

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

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