If the two-digit integer P and Q are positive and have the : PS Archive
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# If the two-digit integer P and Q are positive and have the

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Senior Manager
Joined: 25 Nov 2006
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If the two-digit integer P and Q are positive and have the [#permalink]

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27 Nov 2007, 07:23
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100% (01:08) correct 0% (00:00) wrong based on 3 sessions

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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
Intern
Joined: 25 Nov 2007
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Kudos [?]: 11 [0], given: 0

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27 Nov 2007, 07:29
Its E..

96-69=27
85-58=27
74-47=27
etc...
CEO
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Concentration: Entrepreneurship, Other
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Kudos [?]: 3565 [0], given: 360

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27 Nov 2007, 07:59
E.

P=xy, Q=yx

d=xy-yx=10x+y-10y-x=9x-9y=9(x-y)
only 27 is divisible by 9
CEO
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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.
SVP
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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
16 Dec 2007, 08:33
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