Student: The majority of the 50 students in our class answered at

Question

Student:  The majority of the 50 students in our class answered at least 80% of the questions correctly on last year’s Algebra I final exam. If these final exam scores do accurately measure a student’s level of understanding, Marc must have learned less about algebra last year than most other students in our class, because he answered only 75% of the questions correctly on last year’s Algebra I final exam.
 Which of the following, if true, most seriously weakens the student’s argument?

A. Seven students answered less than 75% of the questions correctly on the final exam in Algebra I last year.
B. Marc is one of four students in the class who did not take an introductory-level algebra course offered by the school two years ago.
C. Marc is one of three students who answered exactly 75% of the questions correctly on the final exam in Algebra I last year.
D. The teacher estimated that last year’s ninth-grade Algebra I final exam was roughly twice as difficult as this year’s Algebra I final exam.
E. Only three students spent less time than Marc spent answering the questions on last year’s Algebra I final exam.

GAngstA · Answer

please explain these options, i got lost in reasoning.

vaibhav1221 · Answer

Hey!

The argument flow: Last year at least 26 students scored 80%+ on the test that accurately measures the student's level of understanding. Marc scored 75%. Therefore, Marc must've learnt less about algebra than most of the students last year.

Though this is not a assumption type question but just for the sake of understanding, let's treat it like that. The argument assumes that all the students who gave the test last year had the same level of knowledge about Algebra to begin with. Without this assumption, the argument falls apart because Marc could've learnt twice as much about algebra than most of the students in the last year yet not enough to get 80%+ questions correct.
I hope this makes sense.

Option B says the exact same thing. Marc did not attend an introductory session on Algebra two years ago. He, therefore, did not have the same level of knowledge about Algebra.
Let's consider numbers.
Assume that a total of 5 topics were taught in the introductory class and a total of 25 topics were taught last year before the test. So, 46 students (Marc was one of the four students who did not attend the introductory sessions) learnt a total of 30 topics in two years but only  25 topics in the last year . Whereas, it is possible that Marc (and maybe even the others but other don't matter here) learnt 25 topics + 3 topics from the introductory class. So, in total  Marc learnt 28 topics last year  whereas  at least 46 students learnt only 25 topics . So, Marc, in this case, learnt more about algebra than most of the students in his class but not enough to get 80%+ questions correct. So, this statement weakens the argument.

Now, let's see the other options independent of the explanation above.

A) Seven students answered less than 75% of the questions correctly on the final exam in Algebra I last year. 
This option doesn't have an impact on the argument at all let alone weaken it. Also, this doesn't talk about Marc at all and neither does Marc fall in the score bracket being discussed. So, completely out of scope.

C) Marc is one of three students who answered exactly 75% of the questions correctly on the final exam in Algebra I last year. 
This option only addresses where Marc stood relative to other students but doesn't say anything about his level of understanding.

D) The teacher estimated that last year’s ninth-grade Algebra I final exam was roughly twice as difficult as this year’s Algebra I final exam. 
The overall difficulty of the exam relative to other exams is completely irrelevant to Marc's performance or his progress relative to other students.

E) Only three students spent less time than Marc spent answering the questions on last year’s Algebra I final exam. 
This is what we could call a filler answer. This is completely irrelevant to what the argument is even talking about.

Option B is the only choice that makes sense through the above explained approach. Also, it is the only option that talks about learning and understanding. Rest of them talk about unrelated things.

I hope this helps.

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Student: The majority of the 50 students in our class answered at

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