Data Sufficiency

If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a.

(2) If b is decreased by 50%, the result is not an integer.

OAC

j_shreyans wrote:If a and b are positive integers, what is the units digit of b ?

(1) b is 25% greater than a.

(2) If b is decreased by 50%, the result is not an integer.

OAC

Statement 1: b is 25% greater than a.
Since b is 1/4 greater than a, a must be a MULTIPLE OF 4, implying the following options for a:
a = 4, 8, 12, 16...
If we increase each of the values by 1/4, we get the following options for b:
b = 5, 10, 15, 20...
The list for b shows that the units digit of b can be 5 or 0.
Since the units digit of b can be different values, INSUFFICIENT.

Statement 2: If b is decreased by 50%, the result is not an integer
If an even integer is reduced by 1/2, the result will be an integer.
2 reduced by 1/2 = 2 - (1/2)2 = 1.
4 reduced by 1/2 = 4 - (1/2)4 = 2.
6 reduced by 1/2 = 6 - (1/2)6 = 3.
Since decreasing b by 1/2 yields a NON-INTEGER, b must be ODD.
Thus, the units digit of b could be 1, 3, 5, 7, or 9.
Since the units digit of b can be different values, INSUFFICIENT.

Statements combined:
Statement 1: The units digit of b must be 5 or 0.
Statement 2: The units digit of b must be odd.
Both statements are satisfied only if the unit digit of b is 5.
SUFFICIENT.

The correct answer is C.