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Need help with a question

Problem Solving — algebra and arithmetic (GMAT Focus Edition)
Expert replies
by nikunjd05 » Sun Jan 23, 2011 6:26 pm
I am going through the Manhattan GMAT Prep, Fractions, Decimals guide, 4th edition. I am still on chapter 1. I am stumped by the In Action question #11. Can some one clarify the answer given?
Thank you.
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Source: — Quantitative Reasoning |

by Tani » Tue Jan 25, 2011 12:13 pm
I would need to see the problem, the answer and the explanation.
Tani Wolff
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by nikunjd05 » Tue Jan 25, 2011 2:02 pm
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.
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