A – B greater than C – D

[sanju09]

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.

What is OA?

[DanaJ]

1. A + D = B + C; subtract B from each side and you get A - B + D = C; now subtract D from each side and you get A - B = C - D. So 1 is sufficient: it tells us that A - B is not greater than C - D, it's equal.

2. is insufficient. Say A = 6 and B = 8, with C = 2 and D = 1. A and B are each greater in value than either C or D, but A - B = -2 and C - D = 1, so A - B is smaller than C - D.
Now let's take another example: say A = 8 and B = 6, with C = 2 and D = 1. Again, the numbers are consistent with statement 2, but this time A - B = 2 is greater than C - D = 1.

So I'd go with A.

[sanju09]

1. A + D = B + C; subtract B from each side and you get A - B + D = C; now subtract D from each side and you get A - B = C - D. So 1 is sufficient: it tells us that A - B is not greater than C - D, it's equal.

2. is insufficient. Say A = 6 and B = 8, with C = 2 and D = 1. A and B are each greater in value than either C or D, but A - B = -2 and C - D = 1, so A - B is smaller than C - D.
Now let's take another example: say A = 8 and B = 6, with C = 2 and D = 1. Again, the numbers are consistent with statement 2, but this time A - B = 2 is greater than C - D = 1.

So I'd go with A.

and you are correct.

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.