pkm9995109794 did a great job of breaking down each answer choice, but unfortunately he made a couple errors which led to not being able to answer the question. I do agree however, that this is a messed up question.
I'll go through it in the same way and use the same numbers so we can all see where the differences are.
Quote:
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.
Firstly, let's pick a few numbers to make our lives easy.
Let the total number of high school seniors in 1997 = 100
Then the number of high school seniors who passed in 1997 = 80 (given)
Then the number of high school seniors who passed in 1998 = 72 (given, decrease of 10%)
Let the total number of high school seniors in 1998 = x
It needs to be noted here that the question is tricky in that it refers to the percentage of students who passed, and also to a percentage decrease in the
number of students who passed. These are two different things. One previous poster incorrectly assumed that this meant that the percentage of students who passed in 1998 was 70%. That is not true.
In fact we don't know what percentage of students passed in 1998. What we DO know is that the percentage of students who passed in 1997 = \(\frac{80}{100} = 80\%\) and that the percentage of students who passed in 1998 was \(\frac{72}{x}\). It will also be helpful to note that if x=90, then the percentage of students who passed in 1998 = \(\frac{72}{90} = 80\%\)
This will be used as a reference when we evaluate the answer choices.
Ok, the question:
The argument above, if true, LEAST supports which of the following statements.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.This is saying that if \(\frac{72}{x}>80\%\), then x<100. Is this true based on the argument?
\(\frac{72}{x}>80\%\) means \(x<\frac{72}{0.8}\) which means \(x< 90\). So x<100, the statement is supported by the argument above.
DISCARDB. 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.This is saying that if \(\frac{72}{x}<80\%\), then x>100. Is this true?
Using the same logic as in A. we can see that here x>90. That means it MIGHT be greater than 100, but is not definitive.
POSSIBLE ANSWER.
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.This is a tricky one. The word "unless" is basically the opposite of "if", or can be read as "if not". So "unless A happens, B happens" should be read as "If not A, then B". Applied to the statement, it can be read as "
If the number of high school seniors was
NOT lower in 1998 than in 1997,
then the number of seniors who passed the exam in 1998 was lower than 80 percent.
Using our numbers, it looks like this: if \(x>100\), then \(\frac{72}{x}<80\%\)
We know if x=90, then 72/x = 80%, so if x>100, then 72/x must be < 80%. Statement is supported by the argument above.
DISCARDD. 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.Number of students who did not pass the exam in 1997 = 20. If this number decreased by more than 10% then the number of students who did not pass the exam in 1998 < 18. (20-10%=18)
Therefore the number of students who did not pass the exam in 1998 = x-72 < 18. Meaning x<90
And the percentage of students who passed the exam in 1998 was greater that 80%. \(\frac{72}{x}>80\%\), and x<90. This is true, supported by the argument above.
DISCARDE. 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.If \(\frac{72}{x}<70\%\), then 100>x
If \(x>\frac{72}{0.7}\), then x<100
If \(x>102\), then \(x<100\). Obviously false.
This statement cannot be true based on the argument above.But now we have a problem. Answer choice B is only partially supported by the argument, and answer choice E is contradicted by the argument. The way the question is phrased, "The argument above, if true, LEAST supports which of the following statements." could be interpreted as "Which of the following statement IS supported by the argument above, but supported the least". That way one could argue that B is the answer. But I don't think that is the correct interpretation of the question, and I'm not sure you can support less than by contradicting, which would suggest to me that
the correct answer should be E, not B.
There could also possibly be a typo in answer choice E, swapping 1997 and 1998 in the second half of the statement. That would result in the statement being fully supported by the argument and the answer would then be a unanimous B.
Can anyone find an error in my analysis?
By the way, to do this in under 2 minutes would take some serious powers of time manipulation...
Cheers