Data Sufficiency

The average grade of students in group 1 is 4.0 while that of students in group 2
is 3.0. If the groups were merged into one big group, what would be the
average grade in this group?

1. There are twice as many students in group 1 as in group 2.
2. There are 4 more students in group 1 than in group 2.

This is a classic weighted average question.

The rule you need to know is this:
If you know the "value" of each of two or more groups (in this case it's the grade), you only need to know the fraction/percent/ratio of each of the groups relative to the others to get the weighted average. You do NOT need to know the actual number of people.

Here, it is enough to know that there are twice as many people in group 1. You could use Statement 2 to find the actual number of people in each group, but that is not relevant.

You can find the answer with formula:
(Fraction/Percent in Group 1) * (Value of Group 1) + (Fraction/Percent in Group 2) * (Value of Group 2)

In this case:
[spoiler](2/3)(4) + (1/3)(3) = x. Statement 1 is Sufficient.[/spoiler]

Statement 2 is not sufficient because knowing the difference does not tell you the fraction or percent. It could be 5 people and 1 person (5/6 in group 1) or it could be 7 people and 3 people (7/10 in group 1).

IMO:A