How many three-digit integers can be divided by 2 to produce a new integer with the same tens digit and units digit as the original integer?
3 digit number divided by 2==>this will yield either a 2 digit number or a 3 digit number
case1:if it yields a 2 digit number
let three digit number =xyz
therefore 2 digit no.=yz===>as unit and tens digit are same
we can write :
100x = 10y+z
clearly this is not possible as LHS is a 3 digit number and RHS is a 2 digit number.
case 2: if it yields a 3 digit number lets say ayz
then we can write
this is only possible if 10y+z =0...and x-2a=0
it means y=z=0..and x=2a
therefore possible values are
a=5=>x=10=>number=1000(its a 4 digit hence not possible)
so only 4 numbers are possible.
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