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

Question

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

Bunuel · Answer

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

So E.

orsang8 · Answer

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

orsang8 · Answer

Whats OA? Please post.

Economist · Answer

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.

Bunuel · Answer

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.

orsang8 · Answer

You are absolutely right Bunuel. My bad. Oh god, I have been making lots of such silly mistakes.

jax91 · Answer

i think the most imp thing in such cases is to consider -ve values.

Its the most common mistake made.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards