Question

This data sufficiency problem consists of a question and two statements labelled (1) and (2), which contain certain data. Using these data and your knowledge of mathematics and everyday facts (such as the number of days in July or the meaning of the word counterclockwise), decide whether the data given are sufficient for answering the question and then indicate one of the following answer choices:

The number A is a two-digit positive integer; the number 8 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 8 is 6.

• A. Data in statement I alone is sufficient.
• B. Data in statement II alone is sufficient.
• C. Data in both statements together is sufficient.
• D. Data in both statements together is not sufficient.

Answer 1

The correct option is B Data in statement II alone is 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 YX, with reversed digits. Writing these numbers in algebraic rather than digital form, you have A = 10 X + Y and B = 10 Y + X.

Therefore, Q= 10B-A = 10(10 Y+ X) -(10 X+ Y) = 100 Y+ 10 X-10 X-Y = 99 Y. The value of Q only depends on the value of Y, which is the tens digit of B. The value ofX is irrelevant to Q. Therefore, statement (2) alone is SUFFICIENT.

You can also test cases to get the same result, although algebra is probably faster ifyou are comfortable with the setup. To test cases here, you'd need to try different two-digit numbers that fit the constraints for each statement:

(1) INSUFFICIENT:

A = 72, B = 27, 10B - A = 198

A = 73, B = 37, 10B - A = 297

(2) SUFFICIENT:

A = 26, B = 62, 10B - A = 594

A = 76, B =67, 10B - A = 594