Critical Reasoning

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.

Man.. very complex answers...I could not finish it in 3mins.
IMO: C.
I felt that all other options provide conditions that are feasible except C. I may be wrong. Please someone explain.

Its not C

IMO E

example:

Total seniors = 100

so in 1997 80% passed i.e. 80
so 20 failed

in 1998 the number of seniors who passed dropped by 10% than what it was in 1997

so seniors who passed in 1998 = 72
seniors who failed in 1998 = ??? (could be anything)

so basically if the pass % is higher in 1998 than in 1997 that means the number of seniors must have decreased

and if the pass % in 1998 lower than 1997 then either the number of seniors did not change or it increased. This statement means that the highest pass % for 1998 can be 72%.

E states that if the pass % is 70% then the number of students in 1998 was less than 1997.

Well, we already know that the number of students who passed in 1998 is 72 so for the pass % to be less than 72, the number of students in 1998 must be more than in 1997.

What is the source of this question ? I am not sure if these kind of questions are that common in the test.

Thanks to GMATKiss for posting such a good question.

Thanks rohangupta83 for your explanation. I followed the same approach as yours and arrived at E. But is there a simpler way (or a much efficient way) to solve this question. Happy that I solved though concerned that I took a lot of time for this one.

Could you guys post your time taken for solving this one.

krishnakumar.ks wrote:Thanks to GMATKiss for posting such a good question.

Thanks rohangupta83 for your explanation. I followed the same approach as yours and arrived at E. But is there a simpler way (or a much efficient way) to solve this question. Happy that I solved though concerned that I took a lot of time for this one.

Could you guys post your time taken for solving this one.

I dont think this one can be done in 2 mins. took me a bit longer as well, would've probably just guessed and moved on if it was in the real exam because the answer choices are long and the correct answer was the last one. So, had to figure all other choices out first.

Hopefully if we get this question but the answer would be A or B

IMO E...

I assumed that the number of last-year students increased from 1997 to 1998 since those who didn't graduate continued to study. Tha fail rate increased as the uathor stated. The choice E provides the least suppost as according to this choice the fail rate should have dicreased in case the number of students increased, which contradicts my assumption and the argument as a whole...

Could somebody please post the OA?

This looks to be more of a quantitative euphoria than a critical reasoning question. Please quote the source and the OA. From another forum, I have noticed that the OA is B. But E seems to be the one that is not supported by the statements in the passage.

According to the argument,

1997: lets say x number of students; 4/5x pass and x/5 fail.
1998: lets say p number of students; 18x/25 pass and ?? fail.

18/25x comes from the fact that number of seniors who passed decreased by 10% from previous year. Previous year number is 4/5x. 18x/25 is what you get if you do the calclations.

A. Percentage of seniors who passed increased from 97 to 98. This means percentage of 98 > that of 97
This means ((18x/25)/ p)* 100 > 80. This means p < (72/80)x ( Not showing the internal calculations here). This means p<x i.e. number of seniors decreased. This is true according to the statements in the passage.

B. ((18x/25)/ p)* 100 < 80. This time inequality sign is reversed. which would lead to p > (72/80)x. Number of high school seniors increased.

C. The statement means: (unless is equivalent to if not) If the number was not lower.....
So, if the number of seniors was higher in 98 than in 97 that means p > x, then number who passed was lower than 80%. This means, ((18x/25)/p)*100 < 80 and this means p > (72/80)x. Although, from this we cannot convincingly say that p > x, but there is a possibility that p > x. Keep this as a contender and lets move forward.


D. ((x/5) - p + (18x/25))> ((10/100) * (x*5)) which comes to p < (9/10)x on simplification and then condition amounts to ( (18x/25)/p) *100) > 80 and this comes to p < (9/10)x . This is also true.

E.The first part evaluates to x < p whereas the second portion evaluates to x > p. So, this is not supported from the data in the passage. This is clearly the LEAST Supported. So choose E.