Data Sufficiency: The number A is a two-digit positive integer; the number B is a 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.
Here is the answer:
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. Write A as XY,
where X and Y are digits (X is the tens digit of A and Y is the units digit of A). Then B can be written as
IT, with reversed digits. Writing these numbers in algebraic rather than digital form, we have A = 1OX + Y
and B = 1OY +X Therefore, Q = 1OB - A = 10(1OY +X) - (1OX + y) = 100Y + 1OX - 1OX - Y= 99Y.
The value of Q only depends on the value of Y, which is the tens digit of B. The value of X is irrelevant to
Q Therefore, statement (2) alone is SUFFICIENT.
You can also make up and test numbers' to get the same result, but algebra is faster and more transparent.
For instance, if we take Y = 7, then Q =9 693, which contains no 7's digits. Thus, it may be hard to see how
Q depends on Y.
Please explain.
Thank you.
