If (65)x = (52)y, then what is the minimum value of x+y ?
Converting both sides to decimal,
6x+5 = 5y+2
We get, 5y - 6x = 3
Now, the first number has 5 and 6 as its digits. So x is definitely greater than 6. The second number has 5 and 2 as its digits. So, y is definitely greater than 5.
So, x can be 7,8,9,10..... and y can be 6,7,8,9.....
By inspection, if we take y as 9 and x as 7, then the equation is satisfied.
So, minimum value of (x+y) should be 16.
Minimum value of x+y is 16