Find the values of x and y so that an odd number of the form 5yxy2x is divisible by both 3 and 5.

Dear Student,

Please find below the solution to the asked query:

Given  : An odd number of the form 5yxy2x is divisible by both 3 and 5.

We know : From divisibility rule for " 5 "  that number can be divisible by 5 if unit digit is 0  or 5 .

So,

x  can  0  or 5 , But also given our number 5yxy2x  is an odd number , So we neglect x  = 0  as at x  = 0  number will became an even number , So

x  = 5  , So our number  : 5y5y25 ,

We know from divisibility rule of 3 that if sum of all digits is divisible by 3 so that number also divisible by 3 . So

5 + y + 5 + y +2 +  5  =  17 + 2 y  Should be divisible by 3

Here we can see at y  = 2 , 5 and 8  we get 17 + 2 y divisible by 3  , So

x  = 5  and y =  2 , 5 and 8                                                                     ( Ans )


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