Quote:
If ♥ represents one of the operations +, −, ×, and ÷, is (a – b) ♥ c = (a ♥ c) – (b ♥ c) for all non-zero integers?
1) c ♥ 0 is undefined.
2) (a + b) ♥ c = (a ♥ c) + (b ♥ c)
KAPLAN OFFICIAL EXPLANATIONAnalyze the question stem
This Yes/No question states that ♥ is one of the four basic math operations and asks whether (a – b) ♥ c equals (a ♥ c) – (b ♥ c) for all non-zero integers. If ♥ is +, then the equation becomes a – b + c = a + c – (b + c) = a – b . This is only true if c = 0, but that is not an allowable value for c. Similarly, if ♥ is –, then a – b – c = a – b. If, on the other hand, ♥ is × or ÷, then you could divide both sides by ♥c to get a – b = a – b. Thus, ♥ must be either multiplication or division in order for the equation to be valid.
Evaluate the statements
Statement (1) says that c ♥ 0 is undefined. The only way for c ♥ 0 to be undefined is if ♥ represents division, since division by 0 is undefined. Statement (1) is sufficient. Eliminate (B), (C), and (E).
Statement (2): Just as is the case for the equation in the question stem, the equation (a + b) ♥ c = (a ♥ c) + (b ♥ c) is only true when ♥ represents multiplication or division. If ♥ represents either multiplication or division, the answer to the question is yes, and that is sufficient. Therefore, (D) is correct.
TAKEAWAY: When a symbol represents an operation, you can plug in the different options for the operation and use logic to determine which one(s) work in the context of the question.