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M31-29

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Bunuel
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M31-29 [#permalink] New post   14 Jun 2015, 14:01
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63% (01:41) correct 38% (01:56) wrong based on 144 sessions
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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.
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Bunuel
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Re M31-29 [#permalink] New post   14 Jun 2015, 14:01
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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.

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 statement implies that the range of heights for all students is equal to the range of heights for male students plus 15 centimeters. Therefore, the height range for all students in the class is 55 centimeters. To clarify this concept further, check the diagram below:

\(-(Shortest \ female)---(Shortest \ male)---(Tallest \ female)-----(Tallest \ male)-\)

Sufficient.


Answer: B
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dsheth7
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Re: M31-29 [#permalink] New post   17 Dec 2016, 05:30
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Hi Buenel.

Please correct me if I am wrong.

Since the shortest girl is 15 cm shorter that the shortest boy and the range of height of boys on 10 greater than the range of girl, thus the tallest student in the class is a boy.

Many thanks.
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Re: M31-29 [#permalink] New post   17 Dec 2016, 11:25
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dsheth7 wrote:
Hi Buenel.

Please correct me if I am wrong.

Since the shortest girl is 15 cm shorter that the shortest boy and the range of height of boys on 10 greater than the range of girl, thus the tallest student in the class is a boy.

Many thanks.


You are right. Also, the tallest boy in that class is 25 cm taller than the tallest girl in that class.
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Re: M31-29 [#permalink] New post   02 Sep 2019, 20:15
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Nice question that can actually make you take more time if you just keep setting up the equations. It is important to realize that averages don't help you get the minimum and maximum values in a set. Averages only talk about the total sum and the total number of elements.
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Re: M31-29 [#permalink] New post   31 Mar 2017, 11:29
My 2 cents:
Hopefully this will help visualize the issue:
1) (w1+…+wf)/f + 10 = (w1+…+wm)/m - Not sufficient

2) Sufficient
|--------fs-----------Ms----------------------fl-----------------------------------Ml------------------
0--------5-----15---20----------------------35----------------------------------60
|--------------------30---------------|
|---------------------------------------40-------------------|
Thanks
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hydr01
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Re: M31-29 [#permalink] New post   11 Mar 2023, 17:37
Shouldn't Statement 1 be sufficient? If we know that the male's average height is 10 cm taller, and that the male's range is 10 cm taller, then the range of the whole class should be 45 cm.

Examples:
1) Male Range = 70 cm - 30 cm = 40 cm, Average = 50 cm
Female Range = 55 cm - 25 cm, Average = 30 cm, Average = 40 cm.
Range of the Whole Class = 70 cm - 25 cm = 45 cm.

2) Male Range = 80 cm - 40 cm = 40 cm, Average = 60 cm
Female Range = 65 cm - 35 cm = 30 cm, Average = 50 cm
Range of the Whole Class = 80 cm - 35 cm = 45 cm

3) Male Range = 90 cm - 50 cm, Average = 70 cm
Female Range = 75 cm - 45 cm, Average = 60 cm
Range of the Whole Class = 90 cm - 45 cm = 45 cm.
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Re: M31-29 [#permalink] New post   12 Mar 2023, 02:37
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hydr01 wrote:
Shouldn't Statement 1 be sufficient? If we know that the male's average height is 10 cm taller, and that the male's range is 10 cm taller, then the range of the whole class should be 45 cm.

Examples:
1) Male Range = 70 cm - 30 cm = 40 cm, Average = 50 cm
Female Range = 55 cm - 25 cm, Average = 30 cm, Average = 40 cm.
Range of the Whole Class = 70 cm - 25 cm = 45 cm.

2) Male Range = 80 cm - 40 cm = 40 cm, Average = 60 cm
Female Range = 65 cm - 35 cm = 30 cm, Average = 50 cm
Range of the Whole Class = 80 cm - 35 cm = 45 cm

3) Male Range = 90 cm - 50 cm, Average = 70 cm
Female Range = 75 cm - 45 cm, Average = 60 cm
Range of the Whole Class = 90 cm - 45 cm = 45 cm.


Males and females in your examples seem to be quite short :lol: OK. Let's assume we have toys.

Two males, 50 and 10 cm tall. The range in this case = 50 - 10 = 40 cm and the average = 30.
Three females 10, 10, and 40 cm tall. The range in this case = 40 - 10 = 30 and the average = 20.
The range of the whole group = 50 - 10 = 40.

Two males, 50 and 10 cm tall. The range in this case = 50 - 10 = 40 and the average = 30.
Three females 5, 20, and 35cm tall. The range in this case = 35 - 5 = 30 and the average = 20.
The range of the whole group = 50 - 5 = 45.

As you can see (1) gives the different total range for the class.
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Re: M31-29 [#permalink] New post   12 Mar 2023, 02:55
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M31-29 [#permalink]
12 Mar 2023, 02:55
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