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Three people took GMAT practice tests in which the minimum a

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Three people took GMAT practice tests in which the minimum a  [#permalink]

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New post 24 Jan 2014, 01:49
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Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 5 times, and no one scored below 500 or over 750. If the individual ranges of the three people's scores in those 5 practice tests were 50, 80 and 120, what is the difference between the maximum and minimum possible ranges of all their scores put together.

A. 50
B. 70
C. 80
D. 120
E. 130
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Re: Three people took GMAT practice tests in which the minimum a  [#permalink]

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New post 24 Jan 2014, 03:21
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flower07 wrote:
Three people took GMAT practice tests in which the minimum and maximum possible scores are 200 and 800, respectively. They each took a test 5 times, and no one scored below 500 or over 750. If the individual ranges of the three people's scores in those 5 practice tests were 50, 80 and 120, what is the difference between the maximum and minimum possible ranges of all their scores put together.

A. 50
B. 70
C. 80
D. 120
E. 130


What is the maximum possible range of all the scores put together?

Well, it's given in the stem itself: no one scored below 500 or over 750 --> range=250.

This can occur, for example, in the following case: if the scores of the first student were from 500 to 550 (range=50), and the scores of say the second student were from 670 to 750 (range=80), then the range of all the scores put together is (max score) - (min score) = 750 - 500 = 250. Notice that here we can even not consider the third student at all.

What is the minimum possible range of all the scores put together?

This is also given: since the individual range of the third student was 120, then the range of all the scores put together cannot possibly be less than that.

This can occur, for example, in the following case: if the scores of the first student were from 500 to 550 (range=50), the scores of the second student were from 500 to 580 (range=80), and the scores of the third student were from 500 to 620 (range=120), then the range of all the scores put together is (max score) - (min score) = 620 - 500 = 120.

Therefore the difference between the maximum and minimum possible ranges of all their scores put together is 250 - 120 = 130.

Answer: E.

Hope it's clear.
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Re: Three people took GMAT practice tests in which the minimum a  [#permalink]

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New post 24 Jan 2014, 01:50
I was successful in understanding this far...

There are three test takers. Each taken the test 5 times. So, there are 15 tests. Ranges for all 3 testers is given : 50, 80 and 120. This means the MAX score - MIN score of all the 5 tests each test takers has taken is 50, 80 and 120 respectively.

What we need to find out is the range of all 15 tests. So, we need the min value and max value of all 15 tests taken by the 3 testers. Is my understanding correct?

Also please explain step by step how to approach this problem. Though I understand the question, I cannot think of any concept to how I can resolve this. Im stumped! :x
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Re: Three people took GMAT practice tests in which the minimum a  [#permalink]

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New post 24 Jan 2014, 20:17
Hi,

Thank you! I understand the 1st paragraph. I have a question in the second paragraph, please.

You said right away that "This is also given: since the individual range of the third student was 120, then the range of all the scores put together cannot possibly be less than that. "

Unless we pick numbers and calculate (like how you did in the paragraph below that statement), how can we say that 120 is the minimum range? or we can conclude 120 is the minimum score only after working it out using the numbers picked?

Thank you!
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Re: Three people took GMAT practice tests in which the minimum a  [#permalink]

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New post 26 Jan 2014, 06:14
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flower07 wrote:
Hi,

Thank you! I understand the 1st paragraph. I have a question in the second paragraph, please.

You said right away that "This is also given: since the individual range of the third student was 120, then the range of all the scores put together cannot possibly be less than that. "

Unless we pick numbers and calculate (like how you did in the paragraph below that statement), how can we say that 120 is the minimum range? or we can conclude 120 is the minimum score only after working it out using the numbers picked?

Thank you!


For this particular problem we don't need to calculate. Ask yourself how can the overall range be less than any of the individual ranges?
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Re: Three people took GMAT practice tests in which the minimum a  [#permalink]

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New post 08 May 2017, 02:28
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We are told :
All 3 students (s1, s2 and s3) scored between 500 and 750 in all the tests
Ranges of each : R1 = 50, R2 = 80 and R3 = 120

Max possible range :
Let’s say s1 scored 500 in one test and his range is 50
So he scored between 500 and 550 in all the tests

Say s2 scored 750 in one test and his range is 120
So he scored between 630 and 750 in all the tests

Third person is irrelevant in this case we have max and min value of their scores
So, Max. possible range = 750 – 500 = 250


Min Possible range :
Lets say s1 scored 750 in one test and his range is 120
So he scored between 630 and 750 in all the tests


Both of the other person can score between 630 and 750 and still be within their range of 80 and 50.

Min range can be 750-630 = 120

So, the difference between Max and Min range = 250 – 120 = 130

Option E
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Re: Three people took GMAT practice tests in which the minimum a  [#permalink]

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