Not convinced with the answer

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Not convinced with the answer

by [email protected] » Tue Nov 19, 2013 7:08 pm
Beginning in 1997, high school seniors in State Q have been required to pass a comprehensive proficiency exam before they are allowed to graduate. The exam requirement was intended to ensure that a minimum level of academic quality will be achieved by the students in the state. In 1997, 20 percent of the seniors did not pass the exam and were, therefore, not allowed to graduate. In 1998, the number of seniors who passed the exam decreased by 10% from the previous year.

The argument above, if true, LEAST supports which of the following statement.

A. If the percentage of high school seniors who passed the exam increased from 1997 to 1998 , the number of high schools seniors decreased during that time period.
B. If the percentage of high school seniors who passed the exam decreased from 1997 to 1998 , the number of high schools seniors increased during that time period.
C. Unless the number of high school seniors was lower in 1998 than in 1997, the number of seniors who passed the exam in 1998 was lower than 80 percent.
D. If the number of high school seniors who did not pass the exam decreased by more than 10 percent from 1997 to 1998, the percentage of high school seniors who passed the exam in 1998 was greater than 80 percent.
E. If the percentage of high school seniors who passed the exam in 1998 was less than 70 percent, the number of high school seniors in 1997 was higher than the number in 1998.

Please provide an explanation with actual numbers.

I think ans is E basis maths that can be derived

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by sahilchaudhary » Wed Nov 20, 2013 9:53 am
I think this question is more about reasoning rather than just numbers. Very confusing and tricky question.

I think the correct answer is C

What is the OA ?
What is the source of this question ?
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by ilyana » Fri Nov 22, 2013 3:49 pm
The answer should be E.

To demonstrate this, I picked some easy numbers.
The information given:
1997:
Total: 100 students
Failed: 20 students
Passed: 80 students

1998:
Total: ?
Failed: ?
Passed: 72 (10% less than in 1997)

General reasoning: we can't say anything about what percentage 72 students are if we don't know the total number of students in 1998. Let total number stay the same (100) and we'll see the result. In this case 72 out of 100 is 72%. If the total number decreases, the percentage is going to grow (from 72%); and if the total number increases, the percentage will plunge down (from the starting point of 72%).

Now, A states that "if the percentage of students who passed the exam increased, ..." What percentage are we talking about? There were 80% of students who passed in 1997, so if the percentage increases, then it should be more than 80%, but calculated with the new total number (total number of students in 1998), which we don't know. However, thanks to our reasoning in the paragraph above, we know that if the total number (of students in 1998) decreases (compared to the number of students in 1997), the percentage (of students who passed) will be more than 72%. We know the percentage - it's more than 80% - so the total number of student must decrease.

B: the crucial percentage as can be seen from above is 72%. Percent increases - total number decreases, percent decreases - total number increases. Let's say that the percentage of students who passed in 1998 is 75% (which is less than 80, but more than 72). Then the total number must decrease. B contradicts this.
B would be correct if it said that percentage decreases not from the starting point of 80%, but from 72%. We should keep in mind this answer. It is supported by given data, but only partially.

C: "Unless the number of high school seniors (I call them "students") was lower in1997 than in 1998, the number (are you sure you copied that right? It should be "percentage") of seniors who passed the exam in 1998 was lower than 80 percent." What it actually says is that if the total number of students grew, then the percentage of students who passed decreased, which is in perfect accordance with our reasoning. If the total number of students grows, the percentage of students who passed is going to be less than 72%, and, of course, less than 80%.

D: if the number of students who failed decreased by more than 10%, then it's going to be less than 18 (10% of 20 students is 2). Then the total number is going to be less than 90. --> the percentage of students passed is going to be more than 80% (72 out of 90 is 80%).

E: the percentage of students who passed in 1998 is less than 70%. The percentage decreases from 72%, then the total number will increase. E states: the total number of students in 1997 is higher; it means that in 1998 it's lower --> it decreased, which contradicts our reasoning totally.

When we compare two answers B and E, we should pick E
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