1997 80% passed, 20% failed
1998 number who passed decreased by 10% from number who passed in 1997
Both in 1997 and 1998 we don't know what was the number of students.

Lets start by taking a number for 1997, say 100 students appeared and 80 passed, 20 failed.
In 1998, we 'll have 10% fewer passing than 1997, so 72 passed the exam.

Now, lets look at the choices.
A - If the percentage of students who passed increased in 1998... so 72 is > 80% of x (x being number of students in 1998.
72 > 0.8x or x<90 so Choice A is valid. Note that the question stem asks for LEAST possible conclusion.

B - %passing decreased. so, 72/x*100 < 80 or 72/x < 0.8 or x>90. x could be 91 or 120. Don't know.

C - Not necessarily true. Number of students can remain the same, say 100 and the number of students passing is less than 80%, ie. 72%.

D - We know that the number of students passing the exam decreased by 10%, lets not evaluate this.

E - The percentage of passing students in 1998 would be less than 70% is when number of students in 1998 is greater than number of students in 1997. >102 to be precise.

Answer would (E)

As in case of B, the conclusion may or may not be true depending upon how much the percentage has decreased. In case of E the number of students in 1997 can not be greater than that in 1998.

This analysis would take more than 5-10 minutes. What's the source and are you sure the OA is B? What's the explanation at the source?

This is a tough one but i'll share my 2 cents.

1997 - 80% pass/ 20% fail.
1998 - 72% pass/ 28% fail. (becasue the number of seniors who passed the exam decreased by 10% from 1997)

After reading options we can observe that only option (B) talks inline with the facts - If the percentage of high school seniors who passed the exam decreased from 1997 to 1998. Rest all talks weird/inconsistent number or percentage.

Let me know your thoughts. Cheers!
_________________

So to make student graduate high school student need to pass an exam
1997 some 20% student failed
In 1998 the result was more bad 10 % “LESS” student pass in comparison to last year ..
So lets assume in 1997 100 high school student were there
1997 ) 80 , 20
1998 ) 72 , X
A ) If this has to be true then there has to be drop in high school student as any thing more then 88 student we cant reach higher %age so thus we can say A is not the least
B ) for this to be true we need passing % to be 79 or less then 79 = so student minimum required is 91 or more .. which makes B as can be or can be not .. defiantly LEAST possible

The answer has to be E. No matter what initial number you pick for the number of students, the range mentioned in E is not possible, hence I figure it is the least possible, possibility being 0. How is the answer B?

Actually I see the light here. Sorry for my earlier posts. Come to think of it, this was pretty straightforward. It is highly confusing because you have to go through all the optins in any case in a question like this, since it asks for the least possible. So many numbers are being talked about and randomly, so I guess this was a reall cracker.

But here is the reason that I think. Here is how:

From Question Stem:
"In 1998, the number of seniors who passed the exam decreased by 10% from the previous year". This is the key statement. We already know that the number of students is less in 1998 than in 1997. Just re-read the statement and it is obvious.

Now Option B says:

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.

We already know that the number of student decreased so B is totally out of the question, the least likely.

This question is tough.
Understand the assumption (hidden statement) is KEY

ANALYZE THE STIMULUS:

Fact: The argument says: In 1997, 20 percent of the seniors did not pass the exam and were, therefore, not allowed to graduate.
Fact: In 1998, the number of seniors who passed the exam decreased by 10% from the previous year.

What the argument implies?
It implies that from 1997 to 1998, the percentage of "NOT passed" the exam is still 20% (KEY), however, the number of seniors passed the exam decreased 10%. Therefore, the total number of high school seniors in 1998 was less than in 1997.

Example to back up
1997: total students: 100, passed: 80, not passed 20 (20%)
1998: total students: X, passed: 72 (less than 10% of 80) = 80% of X. KEY (the argument assumes the percentage of fails is still 20%)
Clearly, X must be fewer than 100.

How the argument can switch the object from "percentage of failed" (variable 1) to "the number of pass" (variable 2) without conflicts?
THE MAIN IDEA IS: The argument MUST FIX one variable to make the other variable be correct. If both variables are not fixed, the logic is out.

Now, we have an idea in mind “any answer that mention the number of students in 1997 is higher than that in 1998 is true”. Answer that mentions the total number of students in 1998 is higher than in 1997 will be out of logic ==> That's the option which will be LEAST supported by the stimulus.

ANALYZE EACH ANSWER:

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.
Wrong. A mentions the number of high school seniors decreased from 1997 to 1998. This is true. So A will be supported by stimulus, hence A is wrong.

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.
Correct. B mentions the case in which the number of high school seniors in 1998 is higher than that in 1997. Thus, B will be least supported by the stimulus. Hence, B is correct.

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.
Wrong. C implies that if the number of high school senior was equal or higher in 1998 than in 1997, the percentage of “passed” will be lower than 80%. It’s correct because the number of “passed” is fixed (10% less than in 1997), total number increases, percentage decreases. That’s the normal logic. C is also supported by the stimulus, hence C is wrong.

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.
Wrong. Sure, it’s true. If the number of “NOT passed” decrease by more than 10% from 1997 to 1998, the percentage of “passed” increased. Thus, the number of high school who passed was greater. D is supported by the stimulus, D is wrong.

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.
Wrong. VERY TEMPTING. E mentions the case in which the number of high school seniors in 1997 was higher than in 1998. It’s clearly be supported by the stimulus, hence E is wrong.

Hope it helps.

The correct answer should be E. I am gonna show that E is not supported in any case and B is sometimes supported:

1997 People who failed 20 %, People who passed 80 % --> 80 (Let's suppose we are dealing with 100 students)
1998 People who failed ?? %, People who passed ?? % --> 72 (10 % fewer students)

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.
Two cases: % of students who pass 75 % --> Total number of students 96 --> Not supported
% of students who pass 60 % --> Total number of students 120 --> Supported
As we can see B is not univocal.

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.

Kudos if you liked it!!!

% of students who pass 70 % --> Total number of students 103 --> Not supported
% of students who pass 20 % --> Total number of students 360 --> Not supported

We can see that E is never supported and B is sometimes.

I think the answer is E. My explanation is in the attached picture.

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.

Given:
In 1997 : 100 STUDENTS = 80 PASSED | 20 FAILED
In 1998 : X students = 72 PASSED | X - 72 FAILED (X CANNOT BE LESS THAN 72)

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.

72 = 80/100 X = 90 thus X should be less than 90, A supports the argument.

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.

X must be greater than 90 to have number of seniors passed below 80% in 1998. number of high school senior increased or decreased can't say.

72---90--(X)--100--(X)-- value of X can lie anywhere above 90.

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.

72---(X)--90--(X)---100 Condition unless the number of seniors lower than 100 in 1998 then 1997... the number of seniors passed in 1998 was lower than 80%... lets say if X is between 90 - 100 pass percentage will be below 80%. e.g. 72 passed out of 95 = pass percentage 75%; if X is below 90 say 80 then 72 passed out of 80 = 90% passed.
Thus conditions does not support both possibilities.

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.
Number of high school seniors failed in 1997 = 20 decreased by more than 10%: means number of high school seniors failed in 1998 less than 18.

in 1998 72 passed + (less than 18 failed = 17 failed) = 89 max limit. 72/89 * 100 = 80.89% approx. if we further reduce failed between 0 - 17 inclusive percentage will increase. thus this option supports the argument.

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.

72 = 70/100 X
X = 102.85 Thus X must be greater than 102.

e.g. if I take X 69%
72=69/100 X
X= 104

SIMILARLY for any percentage below 70 to keep passed student equal to 72. I will have to increase the value of X.
Therefore number of high school seniors in 1997 (100) < number of high school seniors in 1998 (102++)

Therefore E LEAST supported among all.

Yes it is;
The key is to understand that this question requires you to breakdown and assimilate confusingly represented data.
In such cases putting down the logic / data points into manageable bits in your scratch pad/paper will help immensely.

Here's what the data says (I'm assuming that 1997's student strength is 100)
We know that
Pass = 80
Fail = 20

But in 1998 number of pass reduced by 10% of previous year: therefore total number of pass = 72
(note that they haven't told us what the total number of students is)

So let's account for all possibilities:
Student population of 1998 was 1. lower, 2. same, 3. more

Let me assign numbers
1. 80 then
Pass = 72
Fail = 8

2. 100
Pass = 72
Fail = 28

3. 200
Pass = 72
Fail = 128

Now let's look at the options:

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 refers to the second case and this statement is TRUE
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. This is not necessary since if % of passing decreased - total could be equal OR more
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. Case 1 - TRUE
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. This is TRUE - extrapolation of case 1
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. This is TRUE - case 3

Hope that clarifies things!

Ajeeth Peo
Verbal Trainer - CrackVerbal
_________________

Choice E can be supported by the argument.

From the argument:
"In 1998, the number of seniors who passed the exam decreased by 10% from the previous year."

It doesn't matter what number of seniors there are in 1998.

The number of seniors in 1997 is always > the number of seniors in 1998.

The answer is Choice B.

I used 100 as my value for "passed students in '97": so, I'm left with 25 failed and 125 total for '97 ---- and, 90 passed for '98.
Now, Choice B says:

"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 statement is referring to the percentage of high school seniors who passed the exam in '97 and '98, respectively.
In '97, 80% passed ... that's: 100 (passed ~ my "smart number") + 25 (failed) = 125 total.
In '98, let's say: 80% passed ... Now, using the information from the argument: "In 1998, the number of seniors who passed the exam decreased by 10% from the previous year." ...
we have ----> 90 passed ... the MAX value for percentage of seniors who passed in '98 HAS TO BE < 80%.

So ... Let's use 79% to calculate what the total number of students for '98 ... 90=.79T .... The total for '98 < 125 ---- No increase in total number of students.
And, that's all you really need to do, to prove that Choice B is the correct answer. This answer is not supported by the argument.

hello.... with POE i come down to A and B and chose A ...
still not very clear but here's my try...

lets first dissect the plot
97- 80% pass 20% fail
98- 70% pass 30% fail
we need to see actual numbers will follow %ges only if total no remains the same....


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. yup getting support from our dissect

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.totally supporting, we can see clearly if %fail decrease, then %Pass would increase...

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 obviously if less ppl pass then no of studying will be greater

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.yup getting support, but largely vague due to lack of specific info

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.opposite to our dissect.

i was confused in A and B, but can see B clearly.... thank you guys
_________________

This is a messed up question.

Beginning in 1997, high school seniors in State Q have been required to pass a comprehensive proficiency exam before they are allowed to graduate.( it is some fact and let us move on)


The exam requirement was intended to ensure that a minimum level of academic quality will be achieved by the students in the state. ( it is some fact and let us move on)

In 1997, 20 percent of the seniors did not pass the exam and were, therefore, not allowed to graduate. (ok game begins.it says in 1997 20% were not allowed to graduate)

In 1998, the number of seniors who passed the exam decreased by 10% from the previous year.

(So in 1998 NUMBER of seniors decreased by 10%. Suppose there were total 100 seniors in 1997,80 were passed. So 80-8=72 passed in 1998.

Some facts
1.We dont know what % of seniors passed in 1998.
2.We don't know what is the number of seniors who did not pass in 1998.
3.We don't know total number of seniors in 1998

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.[color=#0000ff][/color]

It says IF % of students passed in 98 >% of students passed in 97,then total number of students in 98 is < total number of students in 97.

total students in 97=100
students passed in 97=80

Students passed in 98=80-8=72
total students in 98=X
72 is more than 80% of X.
There fore X<100
So A is supported by argument and a is not the answer.

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.


It says IF % of students passed in 98 < % of students passed in 97,then total number of students in 98 is >total number of students in 97.

let us say

total students in 97=100
Students passed in 97=80
Students passed in 98=80-8=72
total students in 98=X
If 72 is less than 80% of X which means

X should be > 90

If X is between 90 and 100,X need not increase.

So the part of the argument 'then total number of students in 98 is >total number of students in 97.' is wrong.

So B can be the 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.

unless(this is a strong condition) total students in 98 (let us say X) is less than that in 97( 100),number of seniors who passed in 98 (72) should be less than 80%
(These numbers are from calculation shown in B)

which means unless X < 100 then 72 should be less than 80% of X
Actually this need not be correct.

If we take values of X from 99 -91, then still 72 is less than 80% of X .

C can also can be the answer

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.
Let us break the D

If the number of high school seniors who did not pass the exam decreased by more than 10 percent from 1997 to 1998,

passed in 97=80
Total in 98=X

did not pass decreased by 10%=passed increased by 10%

Passed in 98= 88

then the percentage of high school seniors who passed the exam in 1998 was greater than 80 percent.

Which means 88 should be more than 80% of X. But we don know the value of X

this is not supported. Either


D can also be the answer

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.

total in 98=X

Students passed in 98=80-8=72

Those who passed in 98=less than 70% of X


Then minimum value of X=103

so “the number of high school seniors in 1997 was higher than the number in 1998”


E is supported so E is not the answer

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.



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. DISCARD


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.

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. DISCARD


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.

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. DISCARD


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.

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
_________________

Hi,


Q argument may not be messed up but, the OA is actually messed up..




The Requirement -"The argument above, if true, LEAST supports which of the following statements."- does convey that the choice is likely to be supported in whatever little way.
So, B comes close to that requirement. But E is totally incorrect, overtaking B as the most appropriate choice but may not exactly fit into the requirement.
So my take would be that E was not intended by the source as it has turned out to be and, errorneously, 1997 has been mentioned as 1998 and vice-versa.
_________________

This question definitely needs fixing. As others have suggested, switching the years in E would easily make B the answer. If E is really the intended answer, then the question would need to clearly ask for an answer that "MUST BE FALSE." This is not something we'd usually see on the GMAT. In any case, when we're asked for an answer that is "least supported," there should really be four supported answers and one unsupported answer. The relative language "least" is just used to protect the test-writers in case we think of some slight exception or odd interpretation that might make two answers seem valid.
_________________

you can think of a least possible scenario as an except scenario. courtesy of powerscore CR guide.
So Question rephrased : all choices support except one doesn't follow from the argument.

Year Pass Fail Total
97 80 20 100
98 72 ? ?

A. %HSS who passed increased from 97 to 98 --> total number of HSS decreased from 97 to 98
we know number of HSS who passed decreased from 80 to 72. Only way % can increase is the total decrease!
B. %HSS who passed decreased from 97 to 98 --> total number of HSS increased from 97 to 98
if you think of it this is the inverse logic of A. So this should not be supported.
the total number need not decrease for the %HSS to decrease. It can stay the same and still decrease.
from our example with total as 100 in 1998 as well. % of HSS who passed is 72%. Decreased but total stays the same.
C. if total number of seniors who passed in 1998 was greater than or equal to 80%--> number of seniors was lower in 1998 than in 1997.
Only way for % of seniors who passed be greater than 72% in 1998 is if the total number of people decrease. Similar logic to A.
D. if number of HSS who failed decreased by more than 10% from 1997 to 1998 --> % of HSS who passed in 1998 was greater than 80%.
So number of people who failed in 1998 decreased by more than 2 from our premise. So the number decreased to 17,16,15...etc.. So total is 72+17=89, or 88 , or 87....(72/90 =80%) so in all the scenario the percentage of people who passed will be greater than 80%.
E. % of people who passed was less than 70% in 1998--> number of seniors was higher in 97 than in 98.
How can % be less than 70% in 1998? only if total number increase.
if total decreased % will only increase! So option is definitely not supported.

E for me....

Hi,

Responding to a PM...
Lets take a friendly number to check on choices..
Total seniors in 1997 = 100...
80 passed and 20 failed..

1998 - Total = T...
Passed = 90% of 80 = 72 and failed = F...

lets check the 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.
% in 1997 = 80%, and % in \(1998 = \frac{72}{T}\)....
\(\frac{72}{T}\) > 80%.... \(\frac{72}{T}> \frac{80}{100} ..... T < 72*\frac{100}{80}.... T<90\)...
so YES the number of high schools seniors decreased from 100 to LESS than 90 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.
% in 1997 = 80%, and % in 1998 = 72/T....
\(\frac{72}{T} < 80\)%....\(\frac{72}{T}< \frac{80}{100} ..... T > 72*\frac{100}{80}.... T>90...\)
so YES if the number of high schools seniors was 91 and
NO if it was 101 or 110 etc..
So this may not be TRUE everytime....

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.
let T< 100..... so 72/T <80/100..... T>90.....
so if T is between 90 and 100... ans is NO...% <80...
if T is <90... ans is YES > 80%
again Can be TRUE of FALSE..

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.
% in 1997 = 80%, and % in \(1998 = \frac{72}{T}\)....
so # failed in 1997 = 20, and in 1998 #<18, say 17, so T = 72+17 = 89<90..
\(\frac{72}{(<90)}=x\) .... so x> 80%.
so YES 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.
so \(\frac{72}{T}<\frac{70}{100}..............T> 72*\frac{100}{70}.......... T> 102...\) so clearly ans is NO in every case..


Now we have B and C, which may be TRUE or FALSE, and E, which will always be FALSE..
so cleraly E is least supported...

OA given is B and many have found B to be correct..

But answer should be E, unless we mean LEAST supported means that the choice should be supported a bit but not completely..
And I do not think that should be the meaning
_________________

To simplify the argument, let assume total number of seniors in 1997 is 100:

In 1997, 20% seniors did not pass the exam -> 80% pass -> it is 80 pass against 100 in total
In 1998, number of passed senior decreased 10% (of 80) -> it is 72 pass against "X" in total
=> If ratio of passed senior in 1998 equals to that in 1997, then X = 72/80% = 90
If X > 90, then 1998's ratio <80%
If X <90, then 1998's ratio > 80%

We have to eliminate all the answer choices which the above results support or partially support toward:

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.
If 72/X > 80%, then X<100 <=> If X<90, then X<100 (yes, it is always true)
SUPPORT

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.
If 72/X <80%, then X>100 <=> If X>90, then X >100 (Yes, It is true in many cases, but if 100>X>90 it is false)
PARTIALLY SUPPORT

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.
It means if X>=100, then 72/X <80% <=> If X>=100, then X>90 (yes, it is always true)
SUPPORT

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.
It means if the number of no-passed senior (say "n") <18, then (X-n)/X >80% (opp! with variety value of "X" and "n" we know that it can be true or false)
PARTIALLY SUPPORT

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.
If 72/X <70%, 100 > X <=> If X >102.8, then 100> X (wow! it is totally false)
CORRECT ANSWER

It is such the time killer, all about math and easy to be confused, so I wont take time to resolve this kind of question in real test.