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AB and BA are 2 digit integers and AB*BA=CDE, where CDE is a

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AB and BA are 2 digit integers and AB*BA=CDE, where CDE is a [#permalink] New post 09 Aug 2006, 02:48
AB and BA are 2 digit integers and AB*BA=CDE, where CDE is a 3 digit integer. What is AB?

1) A=E
2) A=C
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Re: 2 digit integers [#permalink] New post 09 Aug 2006, 05:24
getzgetzu wrote:
AB and BA are 2 digit integers and AB*BA=CDE, where CDE is a 3 digit integer. What is AB?

1) A=E
2) A=C


(10A+B)(10B+A)=100AB+10(A^2+B^2)+AB =100C+10D+E, neither A not B is equal to 0

(1) If A=E From above AB=E, so AB=A and B=1

But 31*13= 403 and 21*12=252, so clearly we don't know the value of B, it could be any of {1,2,3,4,5,6}

NOT SUFFICIENT

(2) If A=C, the hundreds digit of CDE is A, whereas the hundreds digit of AB*BA is at least AB. For these to be equal, it must be that B=1 and A^2+B^2=A^2+1 must be less than 10

Therefore A^2 is less than 9 i.e A is one of {1,2}

So number AB could be 11 or 21 as 11*11=121 and 21*12=252 satisfy (2). NOT SUFFICIENT


Notcing that if AB is 11 or 21, both (1) and (2) are met, I choose E. If A and B had to be different, (C) would be the answer AB=21, but this is not stated so cannot be assumed.
Re: 2 digit integers   [#permalink] 09 Aug 2006, 05:24
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AB and BA are 2 digit integers and AB*BA=CDE, where CDE is a

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