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

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15 Mar 2012, 22:00
Really tough one....

Good question
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15 Dec 2012, 11:42
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It immediately read like a question beyond Einstein and so with 2.23 already on the clock, chose to say screw it, moving on and selected B because c,d and e suspiciously gave some precise, extra info, so left between A and B, i was like this question is a real B!tch, which starts with B. so imma choose B. where's that meme with a baby pulling a heck yeah fist punch.

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?
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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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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.
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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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17 Jul 2013, 13:29
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Omraan wrote:
hi there
I dont see why B is correct
sounds odd actually
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.

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.

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

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06 Aug 2013, 08:23
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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.
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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29 Oct 2013, 21:30
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I think the answer is E. My explanation is in the attached picture.
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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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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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

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

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17 Jul 2014, 05:04
1
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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!

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

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17 Jul 2014, 05:34
CrackVerbalGMAT wrote:
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

EDIT: I see in your answer that you were already saying that, for E, the number of students is higher in 1998 than in 1997. That's the opposite of what E is saying, so E DOESN'T support the argument, so for me E could be the answer too :/

(don't consider my arguments under this. It's just the same you already said above)

No, your reasoning doesn't work for E. Let's take the same numbers:
1997: 100 students, 80 pass, 20 fail (20%, as in the statement).
1998: the number of students who passed the exam decreased by 10% (as in the statement), so only 72 students passed the exam.
Now, E says the percentage of students who passed the exam in 1998 is less that 70% ("less" means it could also be a very small percentage). So let's take an extreme case and say, for example, it is 10%. If 72 students represent 10% of the total students in 1998, it means there is a total of 720 students in 1998 (of which 648 failed). As 720 is bigger than 100, it is wrong to say "the number of high school seniors in 1997 was higher than the number in 1998". Therefore E is not always true.

Actually, E is more or less the opposite of B: in both cases, you consider a diminution of the percentage of students that pass the exam in 1998 (except E requires the new percentage to be between 0% and 70% whereas B requires the percentage to be between 0% and 80%), but B says it results in an increase of the total number of students compared to 1997 and E says it results in a decrease of that number.
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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12 Aug 2014, 07:44
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?

Well, I got the problem done at around the 2:15 mark ... n, with a bit of luck, I suppose ~

I think the key thing with CR problems dealing with percentages and variables is picking a smart number value and setting up a quick little table.

In this case, I picked "100" for the value of students who passed in '97, and filled out the rest of my chart like this:

(Pass ~ Fail ~ Total)

97: 100 ~ 25 ~ 125
98: 90 ~ ? ~ 90+?

Once I got to this point, I was around the 1:30 mark ~ I quickly saw that Choice A was definitely possible, and X'd it out.
Moved onto B, and luckily, it was the opposite of what Choice A ~~~ And, marked it down. And, skipped the rest.

The best way to do any problem? Of course not, a bit risky, but I was sure that Choice B was an incorrect statement.

Let's call it, an executive decision.
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Re: Beginning in 1997, high school seniors in State Q have been [#permalink]

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13 Aug 2014, 03:25
I think it is better to reduce the percentages to absolute numbers in case of year 1997.
It makes things easier to contradict:
In 1997:
Total = 100
Pass = 80
Fail = 20

In 1998:
Total = X
Pass = 72 (= 90% of 80 = 72% of total students in 1997)
Fail = ??

In case of option B, just assume the total number of students in 1998 remained same, ie, 100. We see that the percentage of students who passed has dropped (to 72% in 1998) WITHOUT an increase in number of students as statement B supposes. However, B is still feasible. If we take total number of students in 1998 as 1000, B holds true.

You can work out the other options, and they come out as true.
I take that back.

Pass in 1998 = 72% of total students in 1997 ...............................(a)

According to E, Pass in 1998 < 70% of total students in 1998
Let Pass in 1998 = 70% of total students in 1998 = 0.7X

From (a),
0.7X = 0.72 * 100
X > 100, ie, X HAS to be greater than 100.
=> E is not supported at all.

Last edited by gaurav90 on 03 Nov 2014, 05:15, edited 1 time in total.
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17 #Top150 CR: Beginning in 1997 high school seniors in State Q 9 23 Sep 2015, 00:44
1 The local high school students have been clamoring for the 6 21 Oct 2012, 13:44
2 Of all the high schools in the United States, Judd Academy 17 23 May 2011, 04:51
Last year, seniors at Jasper County s public high schools 10 27 Jan 2011, 11:48
5 Last year, seniors at Jasper County s public high schools 13 09 Oct 2010, 11:27
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