Bunuel wrote:
The symbol © represents one of the following operations: addition, subtraction, multiplication, or division. What is the value of 4 © 5?
(1) 0 © 1 = 0
(2) 0 © 1 = 1
Kudos for a correct solution.
OFFICIAL SOLUTION:To determine the value of 4 © 5, you have to figure out which of the four operations the symbol represents. The way to do so is to plug each of the operations into the equations offered by each of the two statements and see whether either of them allows you to narrow the symbol down to just one operation.
Statement (1) gives you 0 © 1 = 0. Plug in each operation to see whether any make the equation true. You know addition and subtraction don’t work because you can’t add 1 to or subtract 1 from a number and end up with the same number. However, both multiplication and division work: 0 × 1 = 0, and 0 ÷ 1 = 0. Therefore, statement (1) isn’t sufficient because it doesn’t allow you to narrow the symbol down to just one operation. The answer, then, can’t be A or D.
Statement (2) offers 0 © 1 = 1. The only difference between this equation and the one in statement (1) is the answer. You know that multiplication and division don’t work, because they already produced an answer of zero. Subtraction results in –1, so the only operation that works is addition (0 +1 = 1). This means that statement (2) alone gives you enough information to determine which operation the symbol stands for, which allows you to figure out the
value of 4 © 5.
Correct answer: B.
Data sufficiency questions don’t ask for the actual numeric answer, so don’t take the time to actually determine the value of 4 + 5 (not that it would take you long in this instance).