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TAGS: Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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The range of the heights of the female students in a certain [#permalink]
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Expert's post 00:00

Question Stats: 76% (01:10) correct 24% (01:31) wrong based on 100 sessions
The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the
students in the class?

Indicate all such statements.

A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
C. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.

Practice Questions
Question: 15
Page: 160
Difficulty: hard
[Reveal] Spoiler: OA

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Sandy
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Try our free Online GRE Test Retired Moderator Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: heights of the female students in a certain class is 13.2 in [#permalink]
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Expert's post
Here we have range of heights of males and females in a class.

13.2
A. Shortest Girl |-------------------------| Tallest Girl
|
15.4 |
Shortest Guy |-----------------------------| Tallest Guy
5.8
Since the tallest male student is 5.8 inches taller than taller Female student. Hence we have the range 13.2 +5.8

B. 13.2
Shortest Girl |-------------------------| Tallest Girl

15.4
Shortest Guy |-----------------------------| Tallest Guy

Now we donot know where the median in the two ranges lie. It can be that the median height is close to shortest or tallest depending upon the sample. Hence it is not possible to determine the range.

C. 13.2
Shortest Girl |-------------------------| Tallest Girl

15.4
Shortest Guy |-----------------------------| Tallest Guy

Similar to median we do not know where the average lies either. It can be close to the tallest or the shortest side and we cannot determine the range.
Hence the right answer is A alone.
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Sandy
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Re: heights of the female students in a certain class is 13.2 in [#permalink]
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Expert's post
sandy wrote:
The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the
students in the class?

Indicate all such statements.

A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
C. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.

A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
Let M = the height of the TALLEST male
This means M - 5.8 = the height of the TALLEST female

The range of the heights of the females is 13.2 inches
So, M - 5.8 - 13.2 = the height of the SHORTEST female
Simplify: M - 19 = the height of the SHORTEST female

The range of the heights of the males is 15.4 inches
So, M - 15.4 = the height of the SHORTEST male

Since M - 19 = the height of the SHORTEST female, and M - 15.4 = the height of the SHORTEST male, we can conclude that M - 19 = the height of the SHORTEST STUDENT
We also know that M = the height of the TALLEST STUDENT

So, the range = (height of the TALLEST STUDENT) - (height of the SHORTEST STUDENT)
= M - (M - 19)
= 19
So, the range of all student heights is 19 inches
So, statement A provides SUFFICIENT information to determine the range of all heights.

B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
This is NOT sufficient information.
Consider these two possible cases (since we're aren't told the number of males and females, let's say there are 3 male students and 3 female students):

Case a: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEDIAN height is 51 inches)
The heights of the females is {40, 52.1, 53.2} (notice that the range of heights is 13.2 inches). Here, the MEDIAN height is 52.1 inches)
In this case, the heights of ALL students are: {40, 50, 51, 52.1, 53.2, 65.4}
So, the range of all heights = 65.4 - 40 = 25.4 inches

Case b: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEDIAN height is 51 inches)
The heights of the females are {50, 52.1, 63.2} (notice that the range of heights is 13.2 inches). Here, the MEDIAN height is 52.1 inches)
In this case, the heights of ALL students are: {50, 50, 51, 52.1, 53.2, 65.4}
So, the range of all heights = 65.4 - 50 = 15.4 inches

Since the range can be 25.4 inches OR 15.4 inches, statement B does NOT provides suffient information to determine the range of all heights

C. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.
This is NOT sufficient information.
Consider these two possible cases (since we're aren't told the number of males and females, let's say there are 3 male students and 3 female students):

Case a: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEAN height is 55.5 inches)
The heights of the females is {45, 49.5, 58.2} (notice that the range of heights is 13.2 inches). Here, the MEAN height is 50.9 inches)
In this case, the heights of ALL students are: {45, 49.5, 50, 51, 58.2, 65.4}
So, the range of all heights = 65.4 - 45 = 20.4 inches

Case b: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEAN height is 55.5 inches)
The heights of the females is {44, 51.5, 57.2} (notice that the range of heights is 13.2 inches). Here, the MEAN height is 50.9 inches)
In this case, the heights of ALL students are: {44, 51.5, 50, 51, 57.2, 65.4}
So, the range of all heights = 65.4 - 44 = 21.4 inches

Since the range can be 20.4 inches OR 21.4 inches, statement C does NOT provides suffient information to determine the range of all heights

KEY CONCEPT: Knowing the range of two different populations AND knowing the relative sizes of those populations' median or mean is not enough to determine the range of the COMBINED populations.

Cheers,
Brent
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Re: heights of the female students in a certain class is 13.2 in [#permalink]
GreenlightTestPrep wrote:
sandy wrote:
The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.

Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the
students in the class?

Indicate all such statements.

A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
C. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.

A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
Let M = the height of the TALLEST male
This means M - 5.8 = the height of the TALLEST female

The range of the heights of the females is 13.2 inches
So, M - 5.8 - 13.2 = the height of the SHORTEST female
Simplify: M - 19 = the height of the SHORTEST female

The range of the heights of the males is 15.4 inches
So, M - 15.4 = the height of the SHORTEST male

Since M - 19 = the height of the SHORTEST female, and M - 15.4 = the height of the SHORTEST male, we can conclude that M - 19 = the height of the SHORTEST STUDENT
We also know that M = the height of the TALLEST STUDENT

So, the range = (height of the TALLEST STUDENT) - (height of the SHORTEST STUDENT)
= M - (M - 19)
= 19
So, the range of all student heights is 19 inches
So, statement A provides SUFFICIENT information to determine the range of all heights.

B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
This is NOT sufficient information.
Consider these two possible cases (since we're aren't told the number of males and females, let's say there are 3 male students and 3 female students):

Case a: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEDIAN height is 51 inches)
The heights of the females is {40, 52.1, 53.2} (notice that the range of heights is 13.2 inches). Here, the MEDIAN height is 52.1 inches)
In this case, the heights of ALL students are: {40, 50, 51, 52.1, 53.2, 65.4}
So, the range of all heights = 65.4 - 40 = 25.4 inches

Case b: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEDIAN height is 51 inches)
The heights of the females are {50, 52.1, 63.2} (notice that the range of heights is 13.2 inches). Here, the MEDIAN height is 52.1 inches)
In this case, the heights of ALL students are: {50, 50, 51, 52.1, 53.2, 65.4}
So, the range of all heights = 65.4 - 50 = 15.4 inches

Since the range can be 25.4 inches OR 15.4 inches, statement B does NOT provides suffient information to determine the range of all heights

C. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.
This is NOT sufficient information.
Consider these two possible cases (since we're aren't told the number of males and females, let's say there are 3 male students and 3 female students):

Case a: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEAN height is 55.5 inches)
The heights of the females is {45, 49.5, 58.2} (notice that the range of heights is 13.2 inches). Here, the MEAN height is 50.9 inches)
In this case, the heights of ALL students are: {45, 49.5, 50, 51, 58.2, 65.4}
So, the range of all heights = 65.4 - 45 = 20.4 inches

Case b: The heights of the males are {50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEAN height is 55.5 inches)
The heights of the females is {44, 51.5, 57.2} (notice that the range of heights is 13.2 inches). Here, the MEAN height is 50.9 inches)
In this case, the heights of ALL students are: {44, 51.5, 50, 51, 57.2, 65.4}
So, the range of all heights = 65.4 - 44 = 21.4 inches

Since the range can be 20.4 inches OR 21.4 inches, statement C does NOT provides suffient information to determine the range of all heights

KEY CONCEPT: Knowing the range of two different populations AND knowing the relative sizes of those populations' median or mean is not enough to determine the range of the COMBINED populations.

Cheers,
Brent

Key takeaway from the answer -
Knowing the range of two different populations AND knowing the relative sizes of those populations' median or mean is not enough to determine the range of the COMBINED populations.
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Re: heights of the female students in a certain class is 13.2 in [#permalink]
Only A is sufficient.
Say, we have 6 people - 3 male and 3 female.
[a, b, c], [d, e, f]. By knowing only averages and medians, we can't find combined range
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Re: heights of the female students in a certain class is 13.2 in [#permalink]
Expert's post
The two explanations above provided by sandy and Brent, respectively, are really rock solid.

Thank you.

Regards
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Re: The range of the heights of the female students in a certain [#permalink]
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It helped me to look at solution A visually. I've attached what I did.
Attachments combined range.jpg [ 92.03 KiB | Viewed 3524 times ] Re: The range of the heights of the female students in a certain   [#permalink] 02 Oct 2019, 13:22
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