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Three people each took 5 tests. If the ranges of their score

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Three people each took 5 tests. If the ranges of their score [#permalink] New post 22 Feb 2012, 00:30
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Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35. Oh got the trick.

But my question is If I am thrown a question like this in the test I might panic & try many different kind of values. Is there a particular strategy or pattern for this type of questions.
[Reveal] Spoiler: OA
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 22 Feb 2012, 00:49
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GMATPASSION wrote:
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35. Oh got the trick.

But my question is If I am thrown a question like this in the test I might panic & try many different kind of values. Is there a particular strategy or pattern for this type of questions.


Try to look at it as overlapping sets problem:
# of people in group A is 17;
# of people in group B is 28;
# of people in group C is 35;

What is the minimum # of total people possible in all 3 groups? Clearly if two smaller groups A and B are subsets of bigger group C (so if all people who are in A are also in C and all people who are in B are also in C), then total # of people in all 3 groups will be 35. Minimum # of total people can not possibly be less than 35 since there are already 35 people in group C.

Answer: C.

Hope it's clear.

P.S. Notice that max range for the original question is not limited when the max # of people in all 3 groups for revised question is 17+28+35 (in case there is 0 overlap between the 3 groups).
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 22 Feb 2012, 03:06
Just to clarify the approach here.

It may look like this and would be correct, or?

17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Would be the same minimum range?!?
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 22 Feb 2012, 03:15
Expert's post
MSoS wrote:
Just to clarify the approach here.

It may look like this and would be correct, or?

17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Would be the same minimum range?!?


Yes. The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 21 Aug 2012, 11:16
Hey bunuel,
I am able to get the analogy but I still can't apply that analogy to this case. Kindly explain once more
You said "The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35."
If the one of the possible distribution of marks is mentioned below - then the minimum possible range in scores of the three test-takers should be 7-0 = 7.
17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Thanks in advance
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 22 Aug 2012, 00:27
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fameatop wrote:
Hey bunuel,
I am able to get the analogy but I still can't apply that analogy to this case. Kindly explain once more
You said "The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35."
If the one of the possible distribution of marks is mentioned below - then the minimum possible range in scores of the three test-takers should be 7-0 = 7.
17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Thanks in advance


Your example:
{17, 17, 17, 17, 34} --> range=17;
{7, 7, 7, 7, 35} --> range=28;
{0, 0, 0, 0, 35} --> range=35.

All 15 scores: {0, 0, 0, 0, 7, 7, 7, 7, 17, 17, 17, 17, 34, 35, 35} --> range=35-0=35, not 7.

Hope it's clear.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 23 Aug 2012, 18:12
Bunuel wrote:
fameatop wrote:
Hey bunuel,
I am able to get the analogy but I still can't apply that analogy to this case. Kindly explain once more
You said "The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35."
If the one of the possible distribution of marks is mentioned below - then the minimum possible range in scores of the three test-takers should be 7-0 = 7.
17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Thanks in advance


Your example:
{17, 17, 17, 17, 34} --> range=17;
{7, 7, 7, 7, 35} --> range=28;
{0, 0, 0, 0, 35} --> range=35.

All 15 scores: {0, 0, 0, 0, 7, 7, 7, 7, 17, 17, 17, 17, 34, 35, 35} --> range=35-0=35, not 7.

Hope it's clear.



Hi Bunuel,

Could you explain the similarity b/w this problem and an overlapping set one? I'm not quite sure I understood that correctly..

Thanks
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 24 Aug 2012, 00:46
Expert's post
deliverance wrote:
Bunuel wrote:
fameatop wrote:
Hey bunuel,
I am able to get the analogy but I still can't apply that analogy to this case. Kindly explain once more
You said "The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35."
If the one of the possible distribution of marks is mentioned below - then the minimum possible range in scores of the three test-takers should be 7-0 = 7.
17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Thanks in advance


Your example:
{17, 17, 17, 17, 34} --> range=17;
{7, 7, 7, 7, 35} --> range=28;
{0, 0, 0, 0, 35} --> range=35.

All 15 scores: {0, 0, 0, 0, 7, 7, 7, 7, 17, 17, 17, 17, 34, 35, 35} --> range=35-0=35, not 7.

Hope it's clear.



Hi Bunuel,

Could you explain the similarity b/w this problem and an overlapping set one? I'm not quite sure I understood that correctly..

Thanks


I see no similarities between this problem (statistics) and overlapping sets problems.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 25 Aug 2012, 12:40
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35.


Range = Max-Min
=35-0
=35 ?


Am i right?
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 28 Aug 2012, 00:02
Bunuel wrote:
MSoS wrote:
Just to clarify the approach here.

It may look like this and would be correct, or?

17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Would be the same minimum range?!?


Yes. The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35.


Once again i am assured that quants in GMAT is not about pure math is more about logical thinking. In this particular question i would think about different formulas that could be used, start picking numbers and find different senarios and eventually come up to corrent answer (in best case) or lose 1-2 min and then try to guess (because of time pressure during the test it is difficult stay calm after solving a question for 2 min and coming up with answer which is not in the answer choice).
Bunuel, thank you for such simple explanation. I need to learn to think about the problem for a while first before jumping to solving.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 12 Jan 2013, 06:11
ziko wrote:
Bunuel wrote:
MSoS wrote:
Just to clarify the approach here.

It may look like this and would be correct, or?

17 17 17 17 34
7 7 7 7 35
0 0 0 0 35

Would be the same minimum range?!?


Yes. The main point is that the minimum possible range of the three test-takers can no way be less than the largest range of the three test-takers, which is 35.


Once again i am assured that quants in GMAT is not about pure math is more about logical thinking. In this particular question i would think about different formulas that could be used, start picking numbers and find different senarios and eventually come up to corrent answer (in best case) or lose 1-2 min and then try to guess (because of time pressure during the test it is difficult stay calm after solving a question for 2 min and coming up with answer which is not in the answer choice).
Bunuel, thank you for such simple explanation. I need to learn to think about the problem for a while first before jumping to solving.



Yes, there actually was no math to be applied here, except the concept of "range". The easiest way is simply to figure out how low could the lowest score among the 15 have been, and how high the highest one might have been.

Result is 35(max) - 0(min) = 35, answer C.

Thanks to anyone who clarified this problem.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 12 Jan 2013, 22:14
This problem took me 27 seconds, according to the timer. I took note of my own thinking while I was solving this problem.

I visualized three intervals of length 17, 28, and 35, respectively. Then I felt, intuitively, that the intervals were independent, so I visualized the smaller intervals as covered by the larger one. So I felt that the answer should be the greatest of the numbers. I looked at the numbers again and chose 35. Then I spent a few seconds making sure that I was answering the right question since it seemed too easy.

On an actual exam I would've double-checked myself by coming up with an actual example of fifteen scores, as explained above - provided, of course, that I had enough time.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 15 Apr 2013, 11:37
bugzor wrote:
What would the answer be if it asked for maximum possible range?


It would be impossible to say.
Example: test 1 range 20, test 2 range 50, test 3 range 70.
The test could be on a 100 points range, or on a 1000 points range, and so on...

Let me know if you have doubts...
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 15 Apr 2013, 23:14
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Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

A. 17
B. 28
C. 35
D. 45
E. 80



Another approach is to think of range questions on the number line.

5 numbers have range of 17 means the smallest number and the largest number have a diff of 17 between them. Place them like this on the number line

..................................S1..........(17).............L1..............

5 numbers have range of 28 means the smallest number and the largest number have a diff of 28 between them. Place them like this on the number line

..........................S2...............(28)........................L2..............


5 numbers have range of 35 means the smallest number and the largest number have a diff of 35 between them. Place them like this on the number line


....................S3..................................(35).............................L3..............

The minimum range will be when S1 and L1 and S2 and L2 lie in between S3 and L3. The range of 35 will stay no matter what.

...................S3.......S2.....S1..............................L1......L2.......L3..............

The maximum range, on the other hand, depends on the total range the scores can have. If the score is out of 100, the maximum range will be 100, if they are out of 1000, the maximum range is 1000 and so on.

For example: S1 may lie at 0 and L3 may lie at 100 etc

(0)S1...........................L1..........S2....................................L2..................................S3.......................................................L3(100)
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 16 Oct 2013, 19:36
Hi Bunuel/Karihsma,


Can you please may be explain in a bit more detail the minimum part.
I'm stuck with question of possibilities, I mean what if the first set had this value or that value.

thanks
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 16 Oct 2013, 19:55
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Hi Bunuel/Karihsma,


Can you please may be explain in a bit more detail the minimum part.
I'm stuck with question of possibilities, I mean what if the first set had this value or that value.

thanks


The minimum range of the entire group will be the maximum range of individuals.
Say there are 3 people:
Anna - 30, 38, 45, 46, 47 - Range 17
Beth - 20, 29, 36, 39, 48 - Range 28
Candi - 20, 25, 39, 49, 55 - Range 35

So Candi has 2 scores such that they have a difference of 35 between them (the smallest and the greatest scores).
When we put everyone's scores together and try to find the range, these two scores will still be there. There is a difference of 35 between them and that will stay. So no matter what, the range will be at least 35. In this case the lowest score out of all is 20 and highest is 55 so the range will be 35.

It could be more as well. E.g.

Anna - 30, 38, 45, 46, 47 - Range 17
Beth - 10, 19, 26, 29, 38 - Range 28
Candi - 20, 25, 39, 49, 55 - Range 35

Now taking all scores together, lowest score is 10 and highest is 55 so range becomes 45.

It can keep increasing in this way.
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 27 Apr 2014, 07:18
I simply looked at the 3 different possible scores for each individual test: 17,35,28

We have to find the minimum range:
35-17=8
35-28=7
28-17=11

The find the minimum range, you have to make the set of the 5 scores as small as possible.
Which means that 4 of the 5 scores of each individual person is zero.

7*5 = 35.

Answer C
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 01 May 2014, 20:38
Bunuel wrote:
GMATPASSION wrote:
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35. Oh got the trick.

But my question is If I am thrown a question like this in the test I might panic & try many different kind of values. Is there a particular strategy or pattern for this type of questions.


Try to look at it as overlapping sets problem:
# of people in group A is 17;
# of people in group B is 28;
# of people in group C is 35;

What is the minimum # of total people possible in all 3 groups? Clearly if two smaller groups A and B are subsets of bigger group C (so if all people who are in A are also in C and all people who are in B are also in C), then total # of people in all 3 groups will be 35. Minimum # of total people can not possibly be less than 35 since there are already 35 people in group C.

Answer: C.

Hope it's clear.

P.S. Notice that max range for the original question is not limited when the max # of people in all 3 groups for revised question is 17+28+35 (in case there is 0 overlap between the 3 groups).



Hi Bunuel - Great explanation. Do we have similar kind of questions for practice?
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Re: Three people each took 5 tests. If the ranges of their score [#permalink] New post 02 May 2014, 00:56
Expert's post
chanakya84 wrote:
Bunuel wrote:
GMATPASSION wrote:
Three people each took 5 tests. If the ranges of their scores in the 5 practice tests were 17, 28 and 35, what is the minimum possible range in scores of the three test-takers?

A. 17
B. 28
C. 35
D. 45
E. 80

Min possible range. That means the lowest possible difference in total 15 values.

0 0 0 0 17
0 0 0 0 28
0 0 0 0 35

Minimum possible range is 35. Oh got the trick.

But my question is If I am thrown a question like this in the test I might panic & try many different kind of values. Is there a particular strategy or pattern for this type of questions.


Try to look at it as overlapping sets problem:
# of people in group A is 17;
# of people in group B is 28;
# of people in group C is 35;

What is the minimum # of total people possible in all 3 groups? Clearly if two smaller groups A and B are subsets of bigger group C (so if all people who are in A are also in C and all people who are in B are also in C), then total # of people in all 3 groups will be 35. Minimum # of total people can not possibly be less than 35 since there are already 35 people in group C.

Answer: C.

Hope it's clear.

P.S. Notice that max range for the original question is not limited when the max # of people in all 3 groups for revised question is 17+28+35 (in case there is 0 overlap between the 3 groups).



Hi Bunuel - Great explanation. Do we have similar kind of questions for practice?


Yes, check all min/max questions here: search.php?search_id=tag&tag_id=63

Hope it helps.
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Re: Three people each took 5 tests. If the ranges of their score   [#permalink] 02 May 2014, 00:56
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