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22 Feb 2012, 01:30
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C
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Difficulty:
45%
(medium)
Question Stats:
65% (01:32) correct
35%
(01:56)
wrong
based on 2053
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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
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.
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.
16 Apr 2013, 00:14
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GMATPASSION
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)
22 Feb 2012, 01:49
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GMATPASSION
Consider this as an overlapping sets problem:
- The number of people in Group A is 17.
- The number of people in Group B is 28.
- The number of people in Group C is 35.
What is the minimum number of total people possible in all three groups? Clearly, if the two smaller groups A and B are subsets of the larger group C (meaning all people in A and all in B are also in C), then the total number of people across all three groups would be 35. The minimum total cannot possibly be less than 35, as there are already 35 people in group C.
Answer: C.
Hope it's clear.
P.S. Note that the maximum range for the original question is not limited, whereas the maximum number of people in all three groups for my revised question is 17 + 28 + 35, which occurs if there is zero overlap between the groups.
