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

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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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04 Nov 2011, 22:50
B
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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13 Dec 2011, 10:43
BOWLED !!!...OMG !!! Are we supposed to solve this in 2 mins?...The person who solves such questions within 2 mins is bound to be at least 760...
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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26 Dec 2011, 21:00
neha2785 wrote:
B

Could you please elaborate on the line of reasoning used and the time taken? Any efficient and quick method?
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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26 Dec 2011, 22:58
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
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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26 Dec 2011, 23:59
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?
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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27 Dec 2011, 01:11
prab wrote:
1997 the students who didn't passed 20% (x)
1998 the students who didn't pass was inc. by 10% = X + 10 % of x = y

so how can this be possible, how can the number of passing students dec.
the no# 1. if the number of students decreased...

this is opposed by B

Hence B.

My friend you are forgetting a basic premise of the question. The 10% decrease was in the "NUMBER OF STUDENTS" who passed. So it is 10 % less than the people who graduated in 1997. Lets say in 1997, the number who graduated was 80%. Now lets assume the number who graduated in 1997 was 200. Then the number who graduated in 1998 was 10 percent less, or with this assumed number (200), 20 less people graduated this year. On the opposite end, if the number of those who graduated in 1997 was 200, 200 is 80% of what? of 250. Do the math. So the number who failed were 50, right? So given the information, statement B could hold, or we can still come up with numbers that support the conclusion. The only statement where the maths does not work out is E. So e "LEAST SUPPORTS" the information given.
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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27 Dec 2011, 18:47
easy one
Clearly B
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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15 Mar 2012, 21:40
Eventually got the answer but this took me a lot of time.Is it possible to solve questions like these in under 2 minutes?
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15 Mar 2012, 22:00
Really tough one....

Good question
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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15 Dec 2012, 12:18
Took me over 3 mins to solve! a hard one, but i agree that its B.
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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25 Mar 2013, 13:22
The answer is B, simply because it is not necessarily true. All the others are necessarily true.
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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29 Mar 2013, 04:31
I think most of you are getting it wrong. % increase is not the same as total increase.

Total increase deals with the number of students changing from year to year (absolute value).

Percentage increase deals with the number of students passing and not passing for a given year (relative value).

Check attachment for an in-depth analysis of options A and B.
Attachments

students.pdf [242.23 KiB]

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24 May 2013, 07:59
devinawilliam83 wrote:
Eventually got the answer but this took me a lot of time.Is it possible to solve questions like these in under 2 minutes?

I think the answer is (E)
Pass Fail Total
1997 80 20 100
1998 72( 10% of 80) ? X

Option(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 , lets say the percentage of the passed students is 69% (less than 70) ....so 72/ X *100 = 69 so x has to greater than 100 in order to produce a result =69 or less and the nbr of students in 1997 was 100 hence proved ( E) is least likely .

Option (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.
Let P be Pass percent in 1998 and X is total nbr of students , then P/100 * X =72 and P < 80% , without knowing P we cant for sure say whether X has increased or decreased as there are 2 unknown's .It may be possible or it might not be .

But (E) is impossible option so ans is (E)
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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24 Nov 2013, 22:51
We have to realize, answer is between A and B, and thus discard c,d,e and save time.
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15 Feb 2014, 17:37
devinawilliam83 wrote:
Eventually got the answer but this took me a lot of time.Is it possible to solve questions like these in under 2 minutes?

number vs percentage ...this one is actually very easy
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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16 Apr 2014, 19:53
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.

OA:
[Reveal] Spoiler:
B

THIS QUESTION needs mathematical analysis for all 5 ans options and stimulus as well........any confusion in even one analysis will delay the solution time...
will definitely take more than 2.5- 3 mins for most students....
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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06 May 2014, 09:36

Solution:
Define the following
X # of students in 1997
Y # of students in 1998

The question states that 20% of students did not pass the exam in 1997. Therefore, 80 percent did pass the exam.
And so 0.8X students passed the exam.
In 1998, the number of students who passed the exam was 10% lower in 1998 than in 1997.
Therefore, the number of students who passed the exam in 1998 was (0.9)(0.8)X = 0.72X

Now, (B) is ambiguous.
--> Assume the percentage of high school seniors who passed the exam decreased from 1997 to 1998
That is, (0.72X)/Y < (0.8X)/X
We can cancel X from both sides (permissible since X > 0)
And so, 0.72/Y < 0.8/X
0.72X < 0.8Y
Then Y > (72/80)X (= (9/10)X)
And so this tells us that Y is greater than 90% of X
Thus Y could also be greater than X or X could be greater than Y.

Now, we can disprove (E) (using the same variables)
--> Assume the percentage of high school seniors who passed the exam in 1998 was less than 70 percent.
Then (0.72X)/Y < 0.7
And so, 72X < 70Y
So, (72/70)X < Y
And X < (72/70)X < Y
Thus X < Y
This contradicts the statement given in (E)
Therefore (E) is NOT supported

I apologize for not using latex.
Also, if you're going to post your own questions, please make sure that they are concise, accurate, and unambiguous in order to avoid unnecessary confusion.
If the question were to to ask the reader to identify the answer choice posing the most ambiguity, then indeed (B) would be correct.
Someone please either correct this problem or correct the answer choice in part (E).
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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08 May 2014, 01:23
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.

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17 Jun 2014, 09:38
Why is no one taking into consideration the fact that the students who flunked in 1997 , re-appeared in 1998 thereby increaing the class size
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14 Jul 2014, 23:56
So, just to clarify, if I'm right: B and E are both ABSOLUTELY NOT supporting the statement because they are both wrong, but B is the correct answer because E can be true whereas B is always wrong?

Last edited by Astropi on 17 Jul 2014, 05:34, edited 1 time in total.
Re: Beginning in 1997, high school seniors in State Q have been   [#permalink] 14 Jul 2014, 23:56

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