heshamelaziry wrote:
I didn't understand what he wrote. I need some simple explanation to this question !
The question is:
Each student in a certain sociology class is either an undergraduate student or a graduate student. What percentage of the students in the class are graduate students?
(1) The average score on the final exam for undergraduate students was 20 points lower than the average for all students in the class.
(2) The average score on the final exam for graduate students was 40 points higher than the average for all students in the class.
(1) is clearly insufficient by itself because there is no info about graduate students; (2) is insufficient by itself because there is no info about undergraduate students.
(1) + (2)
Okay, so the concept of weighted average. Let the average for all students be x. Let's call the undergradate students UG; let's call the graduate students G. UG is 20 points below X while G is 40 points above. And, of course, 20 is half of 40.
Then:
UG...X......G
Because UG is twice as close to the "center" as G, there must be twice as many UGs as Gs. (Or, because G is twice as far away from the center than UG, there must be half as many Gs as UGs). So the ratio of UG to G is 2:1. This is a part-to-part ratio. 2 + 1 = 3 is the whole. So 2/3 (or approx 67%) of all students are UGs.
Choose C.
And, of course, if you know the tactic well, and you are really confident, you can pick C without even setting up the UG...X......G diagram.
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This concept shows up quite a bit on the GMAT, and can be applied to other topics that also involve weighted average. For example, average speed of a round trip is a weighted average, and time is the weight. Let's say that from point A to point B there are 100 miles. Let's say a car travels from A to B at 100mph and then returns from B to A at 50 mph. Going from A to B would therefore take the car 1 hour while returning from B to A will take 2 hours. So, the car is travelling at 100 mph for 1 hour and at 50 mph for 2 hours. So, the car's average speed will be the number that is twice as close to 50 than it is to 100, in other words a 2:1 ratio. From 50 to 100, there are 50 units. Dividing 50 into thirds is approximately 17. Therefore, the car's average speed is approx 50 + 17 = 67mph:
50------|-----|-----100
50......67....83....100
