GMAT Math Practice — Algebra Questions
If A, B, C, and D are all positive numbers, is the value of A – B greater than the value of C – D ?
| (1) | A + D = B + C |
| (2) | A and B are each greater in value than either C or D. |
| (A) | Statement (1) ALONE is sufficient to answer the question, but statement (2) alone is NOT sufficient. |
| (B) | Statement (2) ALONE is sufficient to answer the question, but statement (1) alone is NOT sufficient. |
| (C) | BOTH statements (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient. |
| (D) | Each statement ALONE is sufficient to answer the question. |
| (E) | Statements (1) and (2) TOGETHER are NOT sufficient to answer the question. |
Answer and Analysis
The correct response is (A). First, consider statement (1) alone. The equation A + D = B + C is simply another form of the equation A – B = C – D. Given statement (1) alone, the answer to the question must be no.
Next, consider statement (2) alone by substituting simple numbers for the variables. For example, if A, B, C, and D equaled 5, 4, 2, and 1, respectively, then A – B would equal C – D (both expressions would equal 1), and the answer to the question would be no. But if B equaled 3 instead of 4, A – B would be greater than C – D (5 – 3 > 2 – 1), and the answer to the question would be yes. Thus, statement (2) alone is insufficient to answer the question.
