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If the two-digit integer P and Q are positive and have the

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If the two-digit integer P and Q are positive and have the [#permalink] New post 27 Nov 2007, 07:23
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E

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If the two-digit integer P and Q are positive and have the same digits, but in reverse order, which of the following could be the difference between P and Q?

23
24
25
26
27
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 [#permalink] New post 27 Nov 2007, 07:29
Its E..

96-69=27
85-58=27
74-47=27
etc...
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 [#permalink] New post 27 Nov 2007, 07:59
Expert's post
E.

P=xy, Q=yx

d=xy-yx=10x+y-10y-x=9x-9y=9(x-y)
only 27 is divisible by 9
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Re: Multiples PS question [#permalink] New post 27 Nov 2007, 10:08
lumone wrote:
If the two-digit integer P and Q are positive and have the same digits, but in reverse order, which of the following could be the difference between P and Q?

23
24
25
26
27



10x+y - (10y+x) --> 9x-9y 9(x-y) Answer must be divisible by 9. Only 27 works.

E

U could just try random values like 31, 13, 24, 42, etc... but this will take too long, but u may stumble on the answer.
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 [#permalink] New post 16 Dec 2007, 08:33
got E.

p=10t+u
q=10u+t

p-q=9(t-u)

from this you know the answer has to be a multiple of 27. Only E fits the bill
  [#permalink] 16 Dec 2007, 08:33
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