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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
Posts: 333

Kudos [?]: 70 [0], given: 0

Schools: St Gallen, Cambridge, HEC Montreal
If the two-digit integer P and Q are positive and have the [#permalink]

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27 Nov 2007, 08:23
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Question Stats:

100% (00:08) 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

Kudos [?]: 70 [0], given: 0

Intern
Joined: 25 Nov 2007
Posts: 38

Kudos [?]: 12 [0], given: 0

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27 Nov 2007, 08:29
Its E..

96-69=27
85-58=27
74-47=27
etc...

Kudos [?]: 12 [0], given: 0

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4672 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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27 Nov 2007, 08:59
E.

P=xy, Q=yx

d=xy-yx=10x+y-10y-x=9x-9y=9(x-y)
only 27 is divisible by 9

Kudos [?]: 4672 [0], given: 360

CEO
Joined: 29 Mar 2007
Posts: 2553

Kudos [?]: 528 [0], given: 0

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27 Nov 2007, 11:08
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.

Kudos [?]: 528 [0], given: 0

SVP
Joined: 28 Dec 2005
Posts: 1543

Kudos [?]: 186 [0], given: 2

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16 Dec 2007, 09:33
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

Kudos [?]: 186 [0], given: 2

16 Dec 2007, 09:33
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