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TAGS: Retired Moderator Joined: 07 Jun 2014
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The 75th percentile on a test corresponded to a score of 700 [#permalink]
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Expert's post 00:00

Question Stats: 53% (00:43) correct 46% (01:06) wrong based on 89 sessions
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.

 Quantity A Quantity B A 95th percentile score $$800$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

_________________

Sandy
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Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
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Expert's post
Explanation

Scoring scales on a test are not necessarily linear, so do not line up the difference in percentiles with the difference in score; it is not possible to make any predictions about other percentiles.

For all you know, 750 could be the 95th percentile score—or 963 could be. All that is certain is that 25% of the scores are ≤ 450, while 50% of the scores are > 450 and ≤ 700, and 25% of the scores are > 700.
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Sandy
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
"750 could be the 95th percentile score—or 963 could be"

How did you get these limits ? Can you please elaborate? GRE Instructor Joined: 10 Apr 2015
Posts: 3907
Followers: 163

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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
5
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Expert's post
sandy wrote:
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.

 Quantity A Quantity B A 95th percentile score $$800$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

IMPORTANT: Many students will assume that the above distribution of scores is a NORMAL distribution.
However, since this is not mentioned, we can't assume that we have a normal distribution.
This means the scores don't follow any particular pattern (as in a normal distribution)

To begin, let's say there are 100 scores in TOTAL.

NOTE:
If a score of 450 is in the 25th percentile, then 25 scores are less than 450, and...
If a score of 700 is in the 75th percentile, then 75 scores are less than 700

So, it COULD be the case that, when arranged in ASCENDING order, the first 76 value are as follows:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700.....}

The 76 values above satisfy the given information.

The remaining 24 scores can be pretty much anything (as long as they're greater than 700)

So, it COULD be the case that the next 19 values are 701
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, .....}

At this point, we've listed 95 of the 100 values.
So, the next value in the list will be the 95th percentile score.

Consider these two possible cases:

case i: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 702.....}
In this case, 702 is the 95th percentile score.
Since 702 < 800, Quantity B is greater

case ii: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 1,000,000.....}
In this case, 1,000,000 is the 95th percentile score.
Since 1,000,000 > 800, Quantity A is greater

Cheers,
Brent
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Brent Hanneson – Creator of greenlighttestprep.com Founder  Joined: 18 Apr 2015
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
Expert's post
You should deserve more than a kudo Sir., for the amazing , spot-on explanations.

Regards
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
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GreenlightTestPrep wrote:
sandy wrote:
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.

 Quantity A Quantity B A 95th percentile score $$800$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

IMPORTANT: Many students will assume that the above distribution of scores is a NORMAL distribution.
However, since this is not mentioned, we can't assume that we have a normal distribution.
This means the scores don't follow any particular pattern (as in a normal distribution)

To begin, let's say there are 100 scores in TOTAL.

NOTE:
If a score of 450 is in the 25th percentile, then 25 scores are less than 450, and...
If a score of 700 is in the 75th percentile, then 75 scores are less than 700

So, it COULD be the case that, when arranged in ASCENDING order, the first 76 value are as follows:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700.....}

The 76 values above satisfy the given information.

The remaining 24 scores can be pretty much anything (as long as they're greater than 700)

So, it COULD be the case that the next 19 values are 701
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, .....}

At this point, we've listed 95 of the 100 values.
So, the next value in the list will be the 95th percentile score.

Consider these two possible cases:

case i: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 702.....}
In this case, 702 is the 95th percentile score.
Since 702 < 800, Quantity B is greater

case ii: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 1,000,000.....}
In this case, 1,000,000 is the 95th percentile score.
Since 1,000,000 > 800, Quantity A is greater

Cheers,
Brent

Intern Joined: 18 May 2020
Posts: 26
Location: United States
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Kudos [?]: 24 , given: 13

Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
GreenlightTestPrep wrote:
sandy wrote:
The 75th percentile on a test corresponded to a score of 700, while the 25th percentile corresponded to a score of 450.

 Quantity A Quantity B A 95th percentile score $$800$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

IMPORTANT: Many students will assume that the above distribution of scores is a NORMAL distribution.
However, since this is not mentioned, we can't assume that we have a normal distribution.
This means the scores don't follow any particular pattern (as in a normal distribution)

To begin, let's say there are 100 scores in TOTAL.

NOTE:
If a score of 450 is in the 25th percentile, then 25 scores are less than 450, and...
If a score of 700 is in the 75th percentile, then 75 scores are less than 700

So, it COULD be the case that, when arranged in ASCENDING order, the first 76 value are as follows:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700.....}

The 76 values above satisfy the given information.

The remaining 24 scores can be pretty much anything (as long as they're greater than 700)

So, it COULD be the case that the next 19 values are 701
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, .....}

At this point, we've listed 95 of the 100 values.
So, the next value in the list will be the 95th percentile score.

Consider these two possible cases:

case i: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 702.....}
In this case, 702 is the 95th percentile score.
Since 702 < 800, Quantity B is greater

case ii: The values are:
{1,1,1,...(25 1's in total),...1,1,1,450,451,451,451,...(49 451's in total),451,451,451,451...700, 701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701,701, 1,000,000.....}
In this case, 1,000,000 is the 95th percentile score.
Since 1,000,000 > 800, Quantity A is greater

Cheers,
Brent

This was an amazing explanation. I have a small request, just to make my concept clear.

If I attempt this question assuming the scores have a normal distribution, then this is my thought process,

450 is 25%
700 is 75%

700-450 = 250

As they both are equally around the mean, 50% to 75% = 125

700+125 = 825 is ideally what 100% should be ( for linearly distributed graph)

But since this is a normal distribution,

area covered between 50%-75% > area covered between 75-95%

To make them equal, I will have to shift the 95% to the right, which is > 825

It cannot be determined how much > 825 it is supposed to be, hence answer is still D if the above question is modified to a normal distribution.

Please correct me if my thought process is wrong. Thank you.
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
Expert's post
It is indeed correct
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Posts: 26
Location: United States
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Re: The 75th percentile on a test corresponded to a score of 700 [#permalink]
Carcass wrote:
It is indeed correct

Alright! Thank you Re: The 75th percentile on a test corresponded to a score of 700   [#permalink] 03 Jun 2020, 04:55
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