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.
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