This question is a great example of a case where the SAT might try to trap you into doing more work than is necessary. Since the problem asks you whether that mean is exactly 3.0, it is possible to determine this without tedious work. If the average were 3.0, the values on either side of the twelve B (3.0) grades would all even out. And they ALMOST do: there are 6 As (4.0 each) and 6 Cs (2.0 each, so those grades all average out to 3.0); there are 8 A-s and 8 C+s, so those grades (3.7 and 2.3) all average out to 3.0; and there are 11 B+s and 11 B-s, so those all average out to 3. On the list from A on down to C, all those grades average out to 3.0…but then there are the 3 C− grades, and those do not get “averaged out” by anything above an A. So without fully calculating, you can tell that the mean is lower than 3.0. So, we can eliminate “The mean math grade of the 65 students was 3.0.”

Since two of our options deal with the median, we can focus there next. The middle of the 65 terms will be the 33rd term (32 terms above it and 32 terms below it). So when you go from the top down and see that there are 25 grades from A through B+ and then 12 grades of B, you should see that the 33rd term will fall in that group of Bs. This means that the median is 3.0. 

This knowledge allows us to both eliminate “The median math grade of the 65 students is less than a 3.0” and select “The median math grade of the 65 students is higher than the mean math grade of the 65 students.​” Since the mean is somewhat less than 3.0, and the median *is* 3.0, the mean is less than the median.

“If three new students were added to the class and each scored an A, the new class average would be greater than or equal to 3.0” can be eliminated on the logic of the first paragraph: The 62 grades from A down to C all average out to a 3.0, leaving the three C− grades of 1.7 to weigh down that average. In order to balance three 1.7s you’d need three 4.3s; three 4.0s, as this option presents, aren’t quite enough, so the average would still be below 3.0.

This question is an excellent example of a case where the SAT might try to trap us into doing more math than needed. If Henry’s current grades are 3.7, 3.7, 3.3, and 3.0, his current average GPA is lower than needed for him to achieve his goal. (3.7 and 3.3 average to 3.5, so 3.7 and 3.0 will average to lower than 3.5, making his current GPA lower than needed to reach his goal.) So, his final grade needs to bring his average *up* and bridge the gap between his current, below 3.5, average, and his goal. Only “A” has the potential to do so. Keep in mind - A- wasn’t even in the running! So, before you go to tackle complex calculations, make sure you keep in mind that the answer choices are a part of the question, and you’ll want to take a look at what options are even possible before doing the math.