I started with Statement 2. We now know that the fifth exam is worth the same number of points as the first four, but without knowing her current average, we have no way of finding what grade she needs on the last exam. Insufficient.
Statement 1 is tempting: surely if you know the average for the first 4, and you know what the overall average has to be, then you know what the 5th one must be, right? Not exactly. Statement 2 is an important clue: what if the tests AREN'T equally weighted? Let's say the first 4 are worth 100 points each:
Test 1: 71 points
Test 2: 71 points
Test 3: 71 points
Test 4: 71 points
If Test 5 is also worth 100 points, then Deepthi needs 75*5 = 375 total points. She has 284 so far, so on the final test she needs 375 - 284 = 91 points, or 91%.
What if Test 5 is worth 200 points? Then the total number of points available is 600, and she needs .75 * 600 = 450 points. She has 284 so far, so she must receive 450 - 284 = 166 points. 166/200 = 83%. Insufficient.
When we combine the statements, we know the first scenario is correct. Sufficient.
