A can be represented as ab where a is the digit at tens place and b at units place. So, by given information we conclude B = ba (digits in reverse)

A = 10*a + b
B = 10*b + a

Q = 10B - A = 10(10*b + a) - (10*a + b) = 99b where b is the units digit of A or tens digit of B.

From Statement 1, we know the tens digit of A is 7 i.e. a = 7 but we need b as Q = 99b so NOT SUFFICIENT

From Statement 2, we know the tens digit of B is 6 i.e. b = 6 and we need b as Q = 99b = 99*6 so SUFFICIENT

The answer is B

Hope this helps!!

The number A is a two-digit positive integer; the number B is the two-digit positive integer formed by reversing the digits of A. If Q = 10B - A, what is the value of Q?

(1) The tens digit of A is 7.
(2) The tens digit of B is 6.

When a problem asks for the value of a ENTIRE EXPRESSION -- in this case, 10B-A -- be suspicious: quite often there will be insufficient information to determine the values of the individual variables but SUFFICIENT information to determine the value of the ENTIRE EXPRESSION.

In A, let T = the tens digit and U = the units digit.
Then A = 10T+U.
Since B reverses the digits:
B = 10U+T.

Thus:
Q = 10B-A = 10(10U+T)-(10T+U) = (100U+10T) - 10T - U = 99U.

Question rephrased: What is the value of U?

Statement 1: The tens digit of A is 7.
Thus in A, 10T = 10*7, so T=7.
INSUFFICIENT.

Statement 2: The tens digit of B is 6.
Thus in B, 10U = 10*6, so U=6.
SUFFICIENT.

The correct answer is B.