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# M31-29

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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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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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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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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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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 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.
Math Expert
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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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