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by Anju@Gurome » Sun Apr 28, 2013 11:05 pm
vipulgoyal wrote:what is the units digit of p^(xy)

1. Units digit of p^x = 1
2. Units digit of p^y = 1
The tricks to solve this problem are...
  • #1. Units digit of any integral powers of any integer with units digit 1 is always 1.
    #2. p^(xy) = (p^x_^y = (p^y)^x
Statement 1: p^(xy) = (p^x)^y
As units digit of p^x is 1, units digit of (p^x)^y is also 1.

Sufficient

Statement 2: p^(xy) = (p^y)^x
As units digit of p^y is 1, units digit of (p^y)^x is also 1.

Sufficient

The correct answer is D.
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by Matt@VeritasPrep » Wed May 01, 2013 9:35 pm
Just to add a note of caution, the answer actually isn't D, at least not as worded: there's nothing in the stem implying that x and y are integers.

Take statement (1) alone, for instance. If p = 3 and x = 4, then p^x = 81, which has a units digit of 1. But if y is equal to 1/4, then p^(xy) = 3^(4 * 1/4) = 3^1 = 3.

[spoiler]I think the answer is E: one counterexample showing that the units digit of p^(xy) need not be 1 is p = 121, x = 1/2, y = 1/2.[/spoiler]

That said, a lot of definitions of "units digit" seem to restrict this definition to integers: "the units digit is the rightmost digit of the integer". The GMAT may follow this custom (I've never seen them ask about the "units digit" of a non-integer), which would force p^(xy) to be an integer, invalidating my counterexample (though the answer still isn't D.)
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by MBAsa » Fri May 03, 2013 1:32 am
Thanks for that Matt. Totally missed the interger bit
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by Blue_Skies » Fri May 03, 2013 2:46 pm
Thanks Matt.This is another reminder of not to consider any number integer unless otherwise stated.
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