Beginning in 1997, high school seniors in State Q have been required

Can't understand the conclusion and the answer explanations.

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

Let's start with POE-
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 always true. For example, even if pass %age increases from 80 to 81, the total number of students will decrease.
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 may or may not be true. By putting values there can be case when it can and cannot be valid. So, can hold on the option.
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 may or may not be true. By putting values there can be case when it can and cannot be valid. So, can hold on the option.
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 definitely true. I think easiest option to eliminate.
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 always false. If the percentage is even 69.99, still the number of 1997 will not be higher than 1998. Hence this option is correct.

Lets say there were 100 students in 1997. 80 passed and 20 failed.

In 1998, only 72 students passed the exam.
The total number of high school students may vary. So the pass and fail percentage may vary too.
A. If 72 is a higher value of pass percentage then total number of students is smaller than in 1997. True.
B. Similarly, if 72 (number of students passing in 1998) is a smaller percentage than the high school students writing the exam, then the total number of students is higher than that in 1997. True.
C. 72 is 80% for 90 students, which is less than 100. Any number above 90, 72 will be less than 80% of that number. So unless the number of students is less than 90, and thus less than 100, the percentage of students passing is less than 80. True.
D. If the number of students failing is less than 18(less than 10% of 20) , then number of total students writing the exam is <=(less than or equal to) 90 which implies the pass percentage is greater than 80(72/89..or so). True.
E. 72 is less than 70% which means the number of students is more than 102 students, which means the total number of students in 1998 is more than 1997.
Hence False.

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The Story

Beginning in 1997, high school seniors in State Q have been required to pass a comprehensive proficiency exam before they are allowed to graduate. From 1997, there has been a requirement for high school seniors to graduate: they need to pass the mentioned exam.

The exam requirement was intended to ensure that a minimum level of academic quality will be achieved by the students in the state.This statement mentions the intention behind the requirement. The intention was to ensure a minimum level of academic quality in the students.

In 1997, 20 percent of the seniors did not pass the exam and were, therefore, not allowed to graduate.1997, 20% of the high school seniors did not pass the exam. That means 80% passed. Were these 80% students allowed to graduate? No idea. We just know that they met this requirement. Probably, some of these students didn’t meet some other requirement.

In 1998, the number of seniors who passed the exam decreased by 10% from the previous year.This statement compares the number of seniors who passed the exam for two years: 1997 and 1998. If the number of seniors who passed the exam was ‘x’ in 1997, it was 0.9x in 1998.

The Goal

We are looking for an option that is LEAST supported by the information in the passage. This is not a typical question stem. Therefore, before we jump onto the options, let’s be clear how we are going to evaluate the options.

1. Any inference from the given information is going to be INCORRECT. Why? An inference is a statement that is sufficiently supported by the information in the passage.
2. A statement that cannot be inferred but could be true can be the correct answer if the remaining four options are inferences.
3. A statement that contradicts the given information, if it is present in the options, will definitely be the answer to this question.

*Even though the question stem mentions ‘the argument above’, there is no argument given in the stimulus. The stimulus contains a bunch of facts. This question is not an official question, so there can be some lapse in quality.

The Evaluation

(A) Incorrect. The statement talks about a scenario in which the % of seniors who passed the exam increased from 1997 to 1998. In other words, the % of seniors who passed the exam in 1998 was greater than 80%.

Without getting into any numbers or variables, just think about the situation we have. The pass percentage of seniors has increased from 1997 to 1998. However, as given in the passage, the number of seniors who passed the exam has gone down from 1997 to 1998. How can this be possible?

This is possible only if the total number of seniors went down from 1997 to 1998. If the total number of seniors had stayed the same, then, given that the % of seniors who passed has increased, the number of seniors who passed the exam must also have increased. Right?

Thus, given the scenario, we can infer that the number of seniors must have gone down from 1997 to 1998. This is what this option says. Thus, this option can be INFERRED from the passage given.

(B) Incorrect. The statement talks about a scenario in which the % of seniors who passed the exam decreased from 1997 to 1998. In other words, the % of seniors who passed the exam in 1998 was less than 80%.

In this scenario, both the pass percentage of seniors and the number of seniors who passed the exam have gone down. In this scenario, what can we say about the total number of seniors?

The short answer: in this scenario, all three cases are possible:

1. The total number of seniors stayed the same. – It is entirely possible that the number of seniors stayed the same. The number of seniors who passed the exam declined by 10% from 1997 to 1998 since the pass percentage declined from 80% to y%. Can you guess what y will be?

The correct answer is 72%. (Select the text after “is” to show the answer)

2. The total number of seniors increased. – It is possible that the total number of seniors increased. The number of seniors who passed the exam declined by 10% from 1997 to 1998 since the pass percentage declined substantially from 80%. If the number of seniors increased by 44% from 1997 to 1998, what was the pass percentage of seniors in 1998?

The correct answer is 50%. (Select the text after “is” to show the answer)

3. The total number of seniors decreased. – It is also possible that the total number of seniors decreased. The number of seniors who passed the exam declined by 10% from 1997 to 1998 because of a combination of a smaller total number of seniors and a lower pass percentage. Given that the pass percentage of seniors has gone down, is it possible that the number of seniors decreased by 10% or more?

The correct answer is No. (Select the text after “is” to show the answer)

But the total number of seniors can go down by less than 10%.

As we can see, in the scenario presented in this option, all three cases are possible for the total number of seniors. Thus, we CANNOT INFER that the number of high school seniors increased from 1997 to 1998, but it is POSSIBLE that the number of high school seniors increased. If I’m doing this question in the exam, I’ll keep this option on hold. However, after going through all the options, I’ll reject this option since there’s an option that contradicts the information in the passage.

(C) Incorrect. Let’s first understand what this statement means. This statement is of the form: Unless X happened, Y happened. This means that if X did not happen, Y happened.

Thus, the statement means that if the number of high school seniors was NOT lower in 1998 than in 1997, the number of seniors who passed the exam in 1998 was lower than 80 percent.

The scenario considered in this option is that the number of seniors did not decline from 1997 to 1998 i.e. the number of seniors either increased or remained the same.

Now, we know from the passage that the number of seniors who passed the exam declined from 1997 to 1998. Now think about it. How can it happen that the total number of seniors did not decline but the number of seniors who passed the exam declined?

The only way this could happen was when the pass percentage of seniors delined. Think about it. If the pass percentage of seniors did not decline and the total number of seniors also did not decline, there is NO WAY that the number of seniors who passed the exam could have declined. Right?

Thus, we can infer in this scenario that the pass percentage of seniors declined. Thus, we can infer that the pass percentage of seniors in 1998 was lower than 80%. Thus, this option is also an INFERENCE.

(D) Incorrect. This statement talks about a scenario in which the number of seniors who did not pass the exam decreased by more than 10% from 1997 to 1998.

We are already given in the passage that the number of seniors who passed the exam decreased by 10% from 1997 to 1998.

So, we have two types of seniors: seniors who passed the exam (SP) and seniors who did not pass the exam (SNP). We know that SP declined by 10% and that SNP declined by more than 10%.

Think about it. If both SP and SNP had declined by the exact same 10%, then the total number of seniors must also have declined by 10%. Right?

Now, since one component declined by more than 10%, the total number of seniors must also have decreased by more than 10%.

So, we have a scenario in which the total number of seniors went down by more than 10% but the number of seniors who passed the exam went down by only 10%. How is this possible?

The only way this is possible is that the pass percentage went up or increased from 1997 to 1998. Thus, we can infer that the percentage of seniors who passed the exam in 1998 was greater than 80%. This option is, thus, an INFERENCE.

(E) Correct. This option talks about a scenario in which the % of seniors who passed the exam in 1998 was <70%. We know that the same % in 1997 was 80%.

Think about it. Given these pass percentages, if the total number of seniors had stayed the same both the years, can we expect a 10% decline in the number of seniors who passed the exam from 1997 to 1998?

The answer is No. If the total number of seniors stayed the same, then for us to have just 10% decline in the number of seniors who passed the exam, the pass percentage in 1998 has to be 72% (we discussed this in option B as well).

Now, since we know that the pass percentage was not 72% but less than 70%, the number of seniors who passed the exam must have declined more than 10% if the total number of seniors stayed the same.

Right?

For the number of seniors to decline just 10% and not more, the total number of seniors has to go up from 1997 to 1998. Right?

Thus, in this scenario, we can infer that the number of seniors was higher in 1998 than in 1997. This is exactly opposite to what this option says.

Therefore, the given option is CONTRADICTING the given information and is thus the right option.

nightblade354 this one.

how to eliminate D? and how to choose between D and E

OKAY .. lots of maths here..
To start of , understand one thing - the answer would be the one that least likely obeys the statements mentioned in the premise.
If an option is true or could be true , then that is not what we are looking for.
Only if it is definitely wrong , then we can be sure that its least likely to happen and hence our answer.

With the premise it becomes easier to understand if add absolute terms along with percentages here
So assume total population in 1997 of the school to be 100.

Then in 1997
PASS perc = 80 : Fail percent = 20

PASS number = 80 ; FAIL number = 20

IN 1998 - we are given that the number of students who passed decreased by 10 perc
PASS % = ? : FAIL %= ?
PASS NUMBER = 72 ( 10 % less than 80 )
FAIL NUMBER = ?
Also i have used X to show the total students in 1998

Finally coming to the options , remember if an option *COULD* be proven true in any scenario , its not out answer.
A : percentage of high school seniors who passed the exam increased from 1997 to 1998- Lets make it 81%
The number of high school students decreased.
So we are saying that 72 ( number of students who passed in 1998 ) = 81 % of X ( total students )
X= 88.88 or 89
Hence number of high school students decreased.
OUT
B : Exactly opposite of A
percentage of high school seniors who passed the exam decreased from 1997 to 1998 = 70 perc
the number of high schools seniors increased .
So we are saying 72=70% of X
X= 102.85 or 103 , hence increased .
NOTE : here if we had taken decrease of just one percent (79%) - then the population would not have increased but since we need an option that can never be possible , taking 70 percent is justified
OUT

C :The number of seniors who passed the exam in 1998 was lower than 80 percent = 79 %
so we are saying that 72 = 79 % of X
X = 91.11 or 92
Hence a decrease in population going with the statement in C
" the number of high school seniors was lower in 1998 than in 1997 "
OUT

D : number of high school seniors who did not pass the exam decreased by more than 10 percent from 1997 to 1998 = 9 ( number)
" the percentage of high school seniors who passed the exam in 1998 was greater than 80 percent. "
now with the same population number of students who have passed come out as 91 , Hence more than 80%
OUT

E : percentage of high school seniors who passed the exam in 1998 was less than 70 percent = 69 percent
SO 72 = 69% of X
X = 104
but the statement says
" the number of high school seniors in 1997 was higher than the number in 1998.
BUT for any value less than 70 percent the number of high school students must be more in 1998 than in 1997.
Hence this can never be possible
Hence our correct answer.
P.S. - Not something that one can expect to solve under 2mins.

HIT KUDOS if you liked the explanation
Have a great day!

Pls explain this answer as OA mentions E but it isn't so clear

Hey ! Please refer to the explanation above given by merc.
I'm sure you'll understand the reasoning for the QA after that!

Thank-you

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Hi,

Probably, the best explanation to this problem. Thanks!

Srikar

b/w B and E

As we need to choose the least supported, it's E as 'B' can be true in some scenarios.

Time consuming question took me 3.5 mins +

Its a tricky question, but once we decipher the complex terms, its a bit easy to solve.


Below image shows all the cases as mentioned in answer choices A B C D.

only E is wrong as the other way round is true.

Answer : E

Neither B nor E is supported. B can be true, but doesnt have to be.

E is further away though. If the number of students stays the same, the percentage for 98 is already less than 70 %. Actually it could have been less students 98 and still be less than 70 %.

I made a table with one row for each year and the columns:

Number favored (passed)
Percentage favored
Total number of students

Helped a lot!

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Assume there are 100 high school seniors in 1997 (denoted by T-1997)
Fail% in 1997=20% => 20 students failed in 1997( denoted by F-1997)
Pass% in 1997 = 80% => 80 students passed in 1997 (denoted by P-1997)
Pass seniors decreased by 10% as compared to 1997 => 72 passed in 1998(P-1998)
We don't know about Total High school seniors in 1998(T-1998) and failed students in 1998(F-1998). Based on T-1998, percentage of pass and fail in 1998 may be decided.

A) Percentage of senior who passed in 1998 increased from 1997:
What we have:
Pass% of 1997=80%
Pass students of 1998 = 72
Let's assume pass% in 1998 be increased to 90%. This implies 0.9*T-1998=72 => T-1998=80
number of high schools seniors decreased during that time period as T-1997 > T-1998

B) Percentage of senior who passed in 1998 decreased from 1997:
What we have:
Pass% of 1997=80%
Pass students of 1998 = 72
Let's assume pass% in 1998 be increased to 70%. This implies 0.7*T-1998=72 => T-1998=102(approx)
number of high schools seniors increased during that time period as T-1997 < T-1998

C) Pass% in 1998 lower than 80%, if T-1998>T-1997. Consider T-1998 as 101, then P-1998/101= 71% lower than 80%

D) If failed student decreased more than 10% from 1997 to 1998:
We know F-1997= 20, decrement of more than 10%, decrement of more than 2 students in F-1998, so F-1998<18, let's assume F-1998=15
so T-1998= 72+15= 87, Pass% in 1998= 72/87=87%. > 80%

E) Pass% in 1998 is <70%, assume it 60%. 0.6*T-1998=72=> T-1998= 120
T-1998>T-1997. However in the subsequent statement it is given T-1997>T-1998. LEAST SUPPORTED