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What is the units' digit of p^xy? 1). The units' digit of

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What is the units' digit of p^xy? 1). The units' digit of [#permalink]

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New post 05 Oct 2009, 09:41
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A
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C
D
E

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What is the units' digit of p^xy?

1). The units' digit of p^x is 1
2). The units' digit of p^y is 1
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New post 05 Oct 2009, 12:00
1 KUDOS received
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New post 05 Oct 2009, 12:07
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Ans: C

1). The units' digit of p^x is 1
lets say 3^8 x=4 y=2 -> unit digit of 3^4 is 1 but unit digit of 3^8 is 9
insufficient

2). The units' digit of p^y is 1
same as above.

Together:
p^xy= (p^x)^y = (p^y)^x
i.e 1^y=1^x = 1 (any power of 1 is going to be 1)
lets say x=y=4 xy=16
3^4 -> unit digit is 1 for both x or y
81^4 or 3^16 = xxxx6721 -> unit digit is 1
lets say p^x = 221 so any number 221 x 221 x 221 x 221 -> unit digit is going to be always 1.
c is suffcient
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New post 05 Oct 2009, 12:08
Whats OA? Please post.
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Re: Unit's digit [#permalink]

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New post 05 Oct 2009, 12:19
Sorry orsang8, I do not have the OA, got this on some forum. Posted here since it looks interesting :)

If we consider only integers, then you are right, answer should be C.

If we take decimals, eg. p^x = 91.25 then Bunuel is right, answer should be E. No need to consider +ve or -ve sign, units digit is not affected by signs.

Last edited by Economist on 05 Oct 2009, 12:36, edited 1 time in total.
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New post 05 Oct 2009, 12:33
orsang8 wrote:
Ans: C

1). The units' digit of p^x is 1
lets say 3^8 x=4 y=2 -> unit digit of 3^4 is 1 but unit digit of 3^8 is 9
insufficient

2). The units' digit of p^y is 1
same as above.

Together:
p^xy= (p^x)^y = (p^y)^x
i.e 1^y=1^x = 1 (any power of 1 is going to be 1)
lets say x=y=4 xy=16
3^4 -> unit digit is 1 for both x or y
81^4 or 3^16 = xxxx6721 -> unit digit is 1
lets say p^x = 221 so any number 221 x 221 x 221 x 221 -> unit digit is going to be always 1.
c is suffcient


You are assuming p, x, y are positive integers. No ground for this.

p=1/121 x=-1/2=y
p^x=11=p^y

p^(xy)= 1/(121^(1/4)) definitely units digit is not 1.
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New post 05 Oct 2009, 15:11
You are absolutely right Bunuel. My bad. Oh god, I have been making lots of such silly mistakes.
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Re: Unit's digit [#permalink]

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New post 06 Oct 2009, 01:49
i think the most imp thing in such cases is to consider -ve values.

Its the most common mistake made.
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Re: Unit's digit   [#permalink] 06 Oct 2009, 01:49
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