NickHalden wrote:
In a freshman biochemistry class at Newton University, the teacher assigns the class only ‘A’s, ‘B’s’ or ‘C’s. The average on the semester final for the class of 2012 was five points lower than that of the class of 2011. Therefore, the percent of students who received ‘C’s was greater in 2012 than in 2011.
Which of the following, if true, suggests the conclusion above is not necessarily valid?
There was a greater number of students in the 2011 class than in the 2012 class.
The percent of students who received ‘A’s in 2011 was less than in 2012.
Five more students received ‘A’s in 2012 than in 2011.
The same number of students received ‘B’s in 2011 as in 2012.
The percent of students who received ‘B’s was greater in 2012 than in 2011.
There are three grades A, B and C.
The average score was 5 points lower in 2012 than in 2011
Conclusion: Percent of students who got Cs was greater in 2012 than in 2011
Because the average score is lower, the assumption is that more percentage of people got Cs. So it doesn't matter how many people are there in either year. We are talking about the average score and the percentage of students.
We want to weaken the conclusion.
(A) There was a greater number of students in the 2011 class than in the 2012 class.
This, as we discussed above, is irrelevant.
(B) The percent of students who received ‘A’s in 2011 was less than in 2012.
Percent of students who got A in 2012 > Percent of students who got A in 2011
Since average score is lower, more percent of students who got A means more percent of students got C.
Grade A might be given to students getting more than average (simply speaking). If there are more such people, then there will be more people who will get less than average (and hence grade C) to get to the average.
Say these are the scores of 5 people:
3 4 4 4 5
If you have more people getting 5, a higher score, you will need more people to get 3 too to make up the average of 4:
3 3 4 5 5
So option (B) makes our conclusion more likely, not less.
(C) Five more students received ‘A’s in 2012 than in 2011.
Again, numbers are irrelevant.
(D) The same number of students received ‘B’s in 2011 as in 2012.
Numbers are irrelevant.
(E) The percent of students who received ‘B’s was greater in 2012 than in 2011
Even though the average is lower, more percent of students received B's. It is possible that the lower score still gives a B.
IF more people get B (around average), fewer people will get both A's and C's.
Say initially, the scores looked like this: 3 3 4 5 5
If students at average increase, it may look like this: 3 4 4 4 5
Hence percentage of C's may actually decrease.
This weakens our conclusion.
Answer (E)
Can you please explain why the number of people is irrelevant because if I try to prethink then in this passage we are talking about average. so average of 2012 is 5 points lower than 2011. the average can be lower in the following cases:
1. No. of people can be more in 2012.
2. people who have received grade A are more in 2011 class.
3. people who have received grade B or C are more in 2012 class as compared to 2011 class.
Although selected the correct answer, but my reasoning was option E was matching with my prethinking option 3. Am I right in my prethinking? After reading your post, I was not being able to understand why numbers are irrelevant here. Can you please comment?