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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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05 Oct 2009, 08:41
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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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05 Oct 2009, 11:00
Economist wrote:
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

Not as simple as it seems: we know nothing about p,x,y. (integers, positive or negative)

So E.
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05 Oct 2009, 11:07
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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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05 Oct 2009, 11:08
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05 Oct 2009, 11:19
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, 11:36, edited 1 time in total.
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05 Oct 2009, 11:33
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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05 Oct 2009, 14:11
You are absolutely right Bunuel. My bad. Oh god, I have been making lots of such silly mistakes.
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06 Oct 2009, 00:49
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, 00:49
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