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Score range

by karthikpandian19 » Wed Jan 04, 2012 9:48 pm
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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by sam2304 » Wed Jan 04, 2012 11:40 pm
We are asked to find the diff bet minimum and maximum range of the scores.

Minimum range is when all independent scores lies with 120 points either in the 500s side or 750s side. the 120 point is the maximum of the independent score range and 50, 80 comes within that.
S1 - 500-550/700-750
S2 - 500-580/670-750
S3 - 500-620/630-750

Maximum range is when all the scores are spread out between 500 and 750 say
S1 is 500 - 550 (50 range)
S2 is 550 - 630 (80 range)
S3 is 630 - 750 (120 range)

So now minimum range is 120
Maximum range is 250.

250 - 120 = 130

IMO E.

Is it a GMAT Type question ? Seems too tough and took more time for understanding. Hope its the right approach.
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by ariz » Thu Jan 05, 2012 11:32 am
I had diffculty understanding the question as well... glad to see I wasn't the only one
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by santhoshsram » Thu Jan 05, 2012 1:48 pm
E IMO too.

Range will be max if the scores have max spread. We can just pick the extremes to compute this.

Max = 750 - 500 = 250

The min range cannot be less than 120, because one of the three sets already has two scores that are 120 apart and we cant minimize the range any further.

Min = 120

Diff = 250 - 120 = 130 => E

To understand this better, I just imagined the range of each set to be a line segment with length equal to the range.

For example, line1 = 50cms, line2 = 80cms, and line3 = 120 cms.

Now the max range when the three sets are combined is equivalent to arranging these line segments (overlapping) within the allowed limits (500 - 750) so that we form a new line segment that has max length. In this case the max line segment will be 250.

Aside: Max will either be the difference between the allowed limits or the sum of the ranges, whichever is smaller. For example if there ranges of the three sets were 20, 30, 40 the max range would have been 90 not 250.

For the min range, the situation is equivalent to packing the line segment (overlapping) so that we get the minimum possible length. Since we have a line segment of length 120, we cannot come up with any arrangement that has a length less than 120. So min is 120.

I hope this helps. I also hope I haven't ended up confounding this even further.
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by karthikpandian19 » Thu Jan 05, 2012 6:41 pm
OA is E

It is GMAT question taken from 700-750 level questions
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by karthikpandian19 » Thu Jan 05, 2012 6:45 pm
I understood the first part of finding the Max range of 250 ie. 750-500

But still not clear on the Min range of 120???

Can anyone explain?
santhoshsram wrote:E IMO too.

Range will be max if the scores have max spread. We can just pick the extremes to compute this.

Max = 750 - 500 = 250

The min range cannot be less than 120, because one of the three sets already has two scores that are 120 apart and we cant minimize the range any further.

Min = 120

Diff = 250 - 120 = 130 => E

To understand this better, I just imagined the range of each set to be a line segment with length equal to the range.

For example, line1 = 50cms, line2 = 80cms, and line3 = 120 cms.

Now the max range when the three sets are combined is equivalent to arranging these line segments (overlapping) within the allowed limits (500 - 750) so that we form a new line segment that has max length. In this case the max line segment will be 250.

Aside: Max will either be the difference between the allowed limits or the sum of the ranges, whichever is smaller. For example if there ranges of the three sets were 20, 30, 40 the max range would have been 90 not 250.

For the min range, the situation is equivalent to packing the line segment (overlapping) so that we get the minimum possible length. Since we have a line segment of length 120, we cannot come up with any arrangement that has a length less than 120. So min is 120.

I hope this helps. I also hope I haven't ended up confounding this even further.
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by sam2304 » Thu Jan 05, 2012 8:21 pm
karthikpandian19 wrote:I understood the first part of finding the Max range of 250 ie. 750-500

But still not clear on the Min range of 120???

Can anyone explain?
We have 3 students with 5 scores, totally 15 scores are available. We have independent ranges for each student. For overall range to be minimum the independent ranges should overlap each other and for maximum range it should be spread out across the entire 500 - 750. See the pic attached for more clear understanding. Do you get it now ?

So when the independent range overlap it can be anywhere within 500 - 750, we are taking extremes for easy understanding.

S1 is 500 - 550 (S1 range is 50)
S2 is 500 - 580 (s2 range is 80)
S3 is 500 - 620 (s3 range is 120)

All the ranges overlap each other so all the scores lie between 500 to 620 which is the minimum range value 120. Hope this help :)
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Last edited by sam2304 on Thu Jan 05, 2012 8:42 pm, edited 1 time in total.
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by sam2304 » Thu Jan 05, 2012 8:25 pm
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Last edited by sam2304 on Thu Jan 05, 2012 8:43 pm, edited 2 times in total.
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by pemdas » Thu Jan 05, 2012 8:27 pm
i approach a bit diff.
the min. range is the shortest distance within the range of all scores
the max.range is the longest distance accordingly

why 120 cannot be difference but 130 should be

assume 50 or 80 is the lowest possible range to cover only one individual scores (we are looking for all scores' range). 50 (or 80) range can be placed in the middle and inter-connected with 80 (or 50) and 120 ranges respectively (we are looking for the lowest possible).

But 120 placed in the middle will make (250-120-some value)=<130.

We place 50 or 80 range in the middle and distribute either 500-580, 580-630, 630-750 :: 500-620,620-670, 670-750 OR 500-550, 550-630, 630-750 :: 500-620, 620-700, 700-750

we minimize the range covering all scores by three individuals by placing 50 or 80 in the middle of distribution only.

what other posters understood by placing 120-range in the middle and considering parts LHS and RHS from 120-range is that it's allowing for us to get difference between max. and min. ranges only with 120+ estimate, see again (250-120-some value)<=130
karthikpandian19 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
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