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The range of the heights of the female students in a certain class is

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The range of the heights of the female students in a certain class is [#permalink]

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The range of the heights of the female students in a certain class is 30 centimeters, and the range of the heights of the male students in the class is 40 centimeters. What is the range of the heights of all the students in the class?

(1) The average (arithmetic mean) height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.
(2) The shortest female student in the class is 15 centimeters shorter than the shortest male student in the class.
[Reveal] Spoiler: OA

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Re: The range of the heights of the female students in a certain class is [#permalink]

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New post 12 May 2015, 21:51
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I started with the second answer first. The range of a set of numbers is the largest element - the smallest element. So, if the range of the male students in the class is 40 cm then:
40 cm = Tallest_male - Shortest_male
First you have to decide if the tallest female can be taller than the tallest male. This is not the case. If the shortest female is 15 cm shorter than the shortest male and the tallest female is taller than the tallest male then the range of the females would have to be > 40 since the range of male heights would be included in the range of female heights. So, we know that the tallest female is shorter than the tallest male.
If the shortest female is 15 cm shorter than the shortest male then then the range of students is:
Tallest_male - Shortest Female = 60 cm. 40 cm from the range of males and then add 15 cm since the female is 15 cm shorter than the male, and range is the distance from the biggest element to the smallest element.
So, 2 is sufficient

On answer choice one, I came up with two quick examples that showed that the piece of information was not sufficient. (The numbers I came up with make for VERY short males and females! :-D )
Say there are two male students in the class 10 cm tall and 50 cm tall. The range of the male students is 40 cm like it should be. Now suppose there are 3 females in the class with heights of: 10cm, 10cm, 40cm. This gives a range of 30 cm like we are given, and an overall class range of 50 cm (tallest male) - 10 cm (either shortest male or shortest female since they are the same) = 40 cm.

Now keep the set of males the same, and now suppose that the set of females is: 5 cm, 20 cm, and 35 cm. This set still has a range of 35 cm - 5 cm = 30 cm like we are given in the prompt, but now the overall class range is: 50 cm (tallest male) - 5 cm (shortest female) = 45 cm
So, 1 is insufficient.

Therefore my answer is B.
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Re: The range of the heights of the female students in a certain class is [#permalink]

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Let's denote the tallest male, tallest female, shortest male and shortest female as Tm,Tf,Sm & Sf.

From the question stem it can be seen that :-
Tm - Sm = 40
Tf - Sf = 30

Statement 1:
The average height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.

Case I:
Now think about a scenario where you have just two males having height 190 and 150cms so as to satisfy the condition of range being 40; Avg height = 170cms
And you have just two females in class with height 175 and 145 so as to satisfy the condition of range being 30; Avg height = 160cms.

Now we can see that the average height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.

The range of the class in this case will be 190 - 145 = 45

Case II:
But the condition of average height of male being 10 more than average height of female can be achieved in many ways.
For example there are two males 190 and 150 cms.Range is 40 Avg height is 170.
there are 4 females of heights 180,155,155,150 cms. Range is 30. Avg height is 160.
But now the range of the entire class will be 190 -150 = 40

So the range is now different from previous example.
Since we do not know the number of male and female students we cannot determine range of the entire class! So statement 1 is not sufficient.

Statement 2:The shortest female student in the class is 15 centimeters shorter than the shortest male student in the class.


Sm - Sf = 15
This means the tallest female is 15cms taller than shortest male. And we know the longest male is 40 cms taller than shortest male.
This makes it clear that the tallest student in class is Tm and shortest student in class is Sf
So the range of the class will be Tm - Sf

Now from question stem we know that

Tm - Sm = 40
Tm - (15+ Sf) = 40
Tm - Sf = 55

Range of the class is 55. Statement 2 is sufficient.

Answer B

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Re: The range of the heights of the female students in a certain class is [#permalink]

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Bunuel wrote:
The range of the heights of the female students in a certain class is 30 centimeters, and the range of the heights of the male students in the class is 40 centimeters. What is the range of the heights of all the students in the class?

(1) The average (arithmetic mean) height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.
(2) The shortest female student in the class is 15 centimeters shorter than the shortest male student in the class.


Ans: B
Solution: well here we only know the range not the actual values for age.
so lets say shortest Female is F cm and Shortest Male is M cm tall. now because we know the range.
Tallest Female is F+30 cm and Tallest Male is M+40.

1) from statement 1 we can say that only by knowing the arithmetic mean we can not comment on the actual range comparison of the height. plus we have no information about the number of students (total, male, female) so we can not comment on the actual range. [insufficient]

2) from statement 2 we know that F=M-15
now if we put this value in the F+30 we get tallest female as M-15+30= M+15
so now we know the range in terms of M
shortest girl=M-15 and tallest person is the boy who is M+40
range of the class is 55cm. [Sufficient]
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The range of the heights of the female students in a certain class is [#permalink]

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Bunuel wrote:
The range of the heights of the female students in a certain class is 30 centimeters, and the range of the heights of the male students in the class is 40 centimeters. What is the range of the heights of all the students in the class?

(1) The average (arithmetic mean) height of the male students in the class is 10 centimeters greater than the average height of the female students in the class.
(2) The shortest female student in the class is 15 centimeters shorter than the shortest male student in the class.


OFFICIAL SOLUTION:

The range of the heights of the female students in a certain class is 30 centimeters, and the range of the heights of the male students in the class is 40 centimeters. What is the range of the heights of all the students in the class?

(1) The average (arithmetic mean) height of the male students in the class is 10 centimeters greater than the average height of the female students in the class. The averages cannot give the range for the class. Not sufficient.

(2) The shortest female student in the class is 15 centimeters shorter than the shortest male student in the class. This implies that the range of the heights of all the students in the class is the range of the male students plus 15 centimeters, so 55 centimeters. Sufficient.

Answer: B.
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Re: The range of the heights of the female students in a certain class is [#permalink]

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Re: The range of the heights of the female students in a certain class is   [#permalink] 29 Dec 2017, 13:20
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