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# AB and BA are 2-digits integers and AB*BA=CDE, where CDE is

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Senior Manager
Joined: 20 Feb 2006
Posts: 373

Kudos [?]: 38 [0], given: 0

AB and BA are 2-digits integers and AB*BA=CDE, where CDE is [#permalink]

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14 Sep 2006, 02:36
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AB and BA are 2-digits integers and AB*BA=CDE, where CDE is a 3-digits integer. What is AB?
1). A=E
2). A=C

Kudos [?]: 38 [0], given: 0

Retired Moderator
Joined: 05 Jul 2006
Posts: 1748

Kudos [?]: 447 [0], given: 49

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14 Sep 2006, 05:41
AB and BA are 2-digits integers and AB*BA=CDE, where CDE is a 3-digits integer. What is AB?
1). A=E
2). A=C

AB*
BA=
(AB) ( A^2+B^2) (AB) = CDE

THE ONLY USEFULL INFORMATION IS THE UNITS DIGIT OF THE PRODUCT IE: E = (AB)
AND C COULD = (AB) AND THUS C =E =A OR C = (AB) + ANY REMAINDER FROM ( A^2+B^2)

FROM ONE

AB=E,A=E THUS B = 1 and no information can be deducted about A

FROM TWO

A = C NOT SUFF

TOGETHER STILL NOT SUFF

Kudos [?]: 447 [0], given: 49

Senior Manager
Joined: 15 Jul 2006
Posts: 381

Kudos [?]: 1 [0], given: 0

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14 Sep 2006, 05:49
Is it C?

from both 1) and 2) we get:

CB * BC = CDC

the only numbers I can think of fullfilling this condition are 11x11=121

Kudos [?]: 1 [0], given: 0

Senior Manager
Joined: 20 Feb 2006
Posts: 373

Kudos [?]: 38 [0], given: 0

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14 Sep 2006, 06:34
OA is E

Both together still means that AB could still equal 11 or 21

Kudos [?]: 38 [0], given: 0

VP
Joined: 02 Jun 2006
Posts: 1257

Kudos [?]: 110 [0], given: 0

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14 Sep 2006, 07:30
Good job yezz...
I went for C... did't bother to check for 11 x 11
yezz wrote:
AB and BA are 2-digits integers and AB*BA=CDE, where CDE is a 3-digits integer. What is AB?
1). A=E
2). A=C

AB*
BA=
(AB) ( A^2+B^2) (AB) = CDE

THE ONLY USEFULL INFORMATION IS THE UNITS DIGIT OF THE PRODUCT IE: E = (AB)
AND C COULD = (AB) AND THUS C =E =A OR C = (AB) + ANY REMAINDER FROM ( A^2+B^2)

FROM ONE

AB=E,A=E THUS B = 1 and no information can be deducted about A

FROM TWO

A = C NOT SUFF

TOGETHER STILL NOT SUFF

Kudos [?]: 110 [0], given: 0

14 Sep 2006, 07:30
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