Data Sufficiency

If T is an integer between 10 and 100, what is the valueof T ?
(1) The positive difference between TÂ’ digits is 4.
(2) The sum of TÂ’ digits is 12.
OA is E but i guess it should be C. the official answer explians that T could be 48 or 84. but according to statement 1, the positive difference between T's digits is 4. it means it could only be 84 but not 48 because question says positive difference. please correct me if i am wrong.

sana.noor wrote:If T is an integer between 10 and 100, what is the valueof T ?
(1) The positive difference between TÂ’ digits is 4.
(2) The sum of TÂ’ digits is 12.

The POSITIVE DIFFERENCE between x and y = |x-y|.

Let x = the tens digit and y = the units digit.

Statement 1: |x-y| = 4.
It's possible that x=9 and y=5.
In this case, T=95.
It's possible that x=8 and y=4.
In this case, T=84.
Since different values for T are possible, INSUFFICIENT.

Statement 2: x+y = 12.
It's possible that x=8 and y=4.
In this case, T=84.
It's possible that x=9 and y=3.
In this case, T=93.
Since different values for T are possible, INSUFFICIENT.

Statements combined:
Statement 2 implies that x=12-y.
Substituting x=12-y into |x-y| = 4, we get:
|(12-y)-y| = 4
|12-2y| = 4.

Case 1: 12-2y = 4
-2y = -8
y=4, implying that x=8.
In this case, T = 84.

Case 2: -(12-2y) = 4
-12 + 2y = 4
2y = 16
y=8, implying that x=4.
In this case, T = 48.

Since different values for T are possible, INSUFFICIENT.

The correct answer is E.