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Three people each took 5 tests. If the ranges of their score [#permalink]
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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 testtakers? 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.
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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 testtakers?
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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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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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 testtakers can no way be less than the largest range of the three testtakers, 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 testtakers should be 70 = 7. 17 17 17 17 34 7 7 7 7 35 0 0 0 0 35 Thanks in advance
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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 testtakers can no way be less than the largest range of the three testtakers, 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 testtakers should be 70 = 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=350=35, not 7. Hope it's clear.
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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 testtakers can no way be less than the largest range of the three testtakers, 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 testtakers should be 70 = 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=350=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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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 testtakers? 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 = MaxMin =350 =35 ?Am i right?
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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 testtakers can no way be less than the largest range of the three testtakers, 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 12 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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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 testtakers can no way be less than the largest range of the three testtakers, 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 12 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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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 doublechecked 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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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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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 testtakers?
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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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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shankar245 wrote: 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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I simply looked at the 3 different possible scores for each individual test: 17,35,28 We have to find the minimum range: 3517=8 3528= 72817=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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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 testtakers?
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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02 May 2014, 00:56
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 testtakers?
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=63Hope it helps.
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VeritasPrepKarishma wrote: shankar245 wrote: 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. I'm trying to understand this question and the closest I can get to understanding is your answer. However, the original question does not tell us what their individual scores were. It only gives us ranges. Is your explanation still valid if their scores were: Anna: 6, 12, 14, 16, 23  range 17 Beth: 8, 10, 12, 14, 36  range 28 Candi: 10, 12, 14, 20, 45  range 35 Wouldn't now the minimum range be from 645, which is 39? The question tells us the ranges, it seems to me that everyone just assumes that Anna's lowest score was higher than Beth's and Candi's lowest score and that Anna's highest score is also lower than Beth's and Candi's (so that her scores fall right in the middle of the other two's scores and so on). Thank you!



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wodan wrote: VeritasPrepKarishma wrote: shankar245 wrote: 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. I'm trying to understand this question and the closest I can get to understanding is your answer. However, the original question does not tell us what their individual scores were. It only gives us ranges. Is your explanation still valid if their scores were: Anna: 6, 12, 14, 16, 23  range 17 Beth: 8, 10, 12, 14, 36  range 28 Candi: 10, 12, 14, 20, 45  range 35 Wouldn't now the minimum range be from 645, which is 39? The question tells us the ranges, it seems to me that everyone just assumes that Anna's lowest score was higher than Beth's and Candi's lowest score and that Anna's highest score is also lower than Beth's and Candi's (so that her scores fall right in the middle of the other two's scores and so on). Thank you! Yes, you are right that in this case the range will be 39. But note that we are looking for the minimum possible range. Is it possible to reduce the range? Yes. Try to make it as small as possible. Make Anna's and Beth's lowest scores higher than Candi's lowest score and make their highest scores lower than Candi's highest score. That ways, you can reduce the range of all scores to Candi's range.
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