Question

a 5 digit number with digits a, b, c, d, e i.e. abcde when multiplied by 4 becomes edcba. find a, b, c, d, e?

Answer 1

First, A must not be greater than 2, becaue then 4*ABCDE will have 6 digits, and it cannot be 1 becaue it is the unit digit of EDCBA.

Now E must be 8.

B must be odd, so BA can be divisible by 4, it should be 1 so AB * 4 will not exceed 90. (23 * 4) = 92

21CD8 * 4= 8DC12

8*4 = 32, therefor 4D must end with 8. D can only be 2 or 7.

21C28 * 4 = 82C12

Impossible because 21*4 = 84, so D = 7

21C78 * 4 = 87C12.  

Now, because the sum of digits hasen't changed by multiplying the number by 4, ABCDE must be divisible by 9.  

So c must be either 0 or 9

78 * 4 = 312, so it's impossible that C is zero, how about 9?  

Yes, it works!!!  

ABCDE = 21978