# Math forum

 A unique number Options
mohit
 #1 Posted : Sunday, March 20, 2011 1:45:03 PM

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Posts: 44

A FOUR DIGIT NUMBER , WHEN MULTIPLIED BY THE LAST DIGIT GIVES A NUMBER WHICH IS REVERSE OF THE ORIGINAL NUMBER........
NOTE: ALL DIGITS ARE DIFFERENT.
WHAT IS THE NUMBER?
EXAMPLE:
ABCD is the number.
ABCD * D =DCBA..

kennysoccer25
 #2 Posted : Sunday, March 20, 2011 4:30:00 PM
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clearly A = 1 otherwise A*D =/= D

with that in mind D*D = A (mod 10) -> D = 1 (n/a) or 9

ABCD * D = DCBA -> 1BC9 * 9 = 9CB1

AB * D < 100 only if B = 0 or 1 (n/a)

10C9*9=9C01

C = 8 (divisibility rule of 9 - sum of digits of a multiple of 9 is also divisible by 9)

1089 * 9 = 9801 (easily checkable)

mohit
 #3 Posted : Monday, March 21, 2011 7:30:36 AM

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Joined: 3/16/2011
Posts: 44

yupes thts correct..the answer in 1089...

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