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24 Jan 2014, 01:49
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E
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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
A. 50
B. 70
C. 80
D. 120
E. 130
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24 Jan 2014, 03:21
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flower07
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.
27 Nov 2021, 07:20
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flower07
Let's call the students A, B and C
SMALLEST RANGE
The smallest range occurs when there is complete overlap of scores.
For example let's say that:
- Student A's scores range from 500 to 550 (range of 50)
- Student B's scores range from 500 to 580 (range of 80)
- Student C's scores range from 500 to 620 (range of 120)
So, when we combine scores of all three students, the 15 scores range from 500 to 620.
Here, the range = 620 - 500 = 120
GREATEST RANGE
The smallest range occurs when there is zero overlap of scores.
For example let's say that:
- Student A's scores range from 500 to 550 (range of 50)
- Student B's scores range from 550 to 630 (range of 80)
- Student C's scores range from 630 to 750 (range of 120)
So, when we combine scores of all three students, the 15 scores range from 500 to 750.
Here, the range = 750 - 500 = 250
The difference between the maximum and minimum possible ranges = 250 - 120 = 130
Answer: E
