Max has $125 consisting of bills each worth either $5 or $20. How many bills worth $5 does Max have?
(1) Max has fewer than 5 bills worth $5 each.
(2) Max has more than 5 bills worth $20 each.
125 = 5x + 20y
x = ?
the units digit of 125 is 5. From the equation 20y will always yield a value with 0 as it's units digit.
While 5x will then have to yield a value that ends with 5.
(1) if x is less than 5 then, we can choose from 0,1,2,3,4 but 5x should end with 5 so, we are left with 1 and 3 as possibilities.
Let x=1, the 20y should be 120, y=6
let x=3, then 5x=15 so 20y should be 125-15=110. But 110 is not a multiple of 20 so, not possible.
Thus, x=1. SUFFICIENT
(2) if y is greater than 5
Let us try y=6, this is possible!
Let us try y=7, 20y = 140, this is not possible or our eq.
thus, y=6. SUFFICIENT
Impossible is nothing to God.