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The average of set S comprising 5 non-zero integers is 0. What is its 22 Sep 2019, 12:17
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C
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65% (hard)

Question Stats:

52% (02:07) correct 48% (02:10) wrong based on 67 sessions

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The average of set S comprising 5 non-zero integers is 0. What is its median?
1) The range of set S is 3
2) Set S has a unique mode that is positive
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C
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Archit3110
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The average of set S comprising 5 non-zero integers is 0. What is its Updated on: 01 Oct 2019, 08:00
Originally posted by Archit3110 on 30 Sep 2019, 17:50.
Last edited by Archit3110 on 01 Oct 2019, 08:00, edited 2 times in total.
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Asad
The average of set S comprising 5 non-zero integers is 0. What is its median?
1) The range of set S is 3
2) Set S has a unique mode that is positive


#1
The range of set S is 3
-2,-1,1,1,1
2,1,-1,-1,-1
insufficient
#2
Set S has a unique mode that is positive
it can be any set value with mode of +ve value insufficient
from 1 &2
only possible set value -2,-1,1,1,1
median ; 1
IMO C
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The average of set S comprising 5 non-zero integers is 0. What is its 30 Sep 2019, 21:42
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the set value satisfy with both requirements is [-2,-1,1,1,1]
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The average of set S comprising 5 non-zero integers is 0. What is its 01 Oct 2019, 02:23
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Archit3110
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The average of set S comprising 5 non-zero integers is 0. What is its median?
1) The range of set S is 3
2) Set S has a unique mode that is positive


I am not able to figure out what would be the set value which satisfies both the given statement

The set can be many as the digits need not be distinct, so -2, -1, 1,1,1...

The average of set S comprising 5 non-zero integers is 0. What is its median?

1) The range of set S is 3
It could be .. -1, -1, 0, 0, 2, but numbers are non-zero
or -2, -1, 1, 1, 1..
or 2,1, -1, -1, -1

2) Set S has a unique mode that is positive
-5, 1, 1, 1, 2 or -4, 1, 1, 1, 1

Combined..
If the numbers are in ascending order a, b, c, d, e.....a+b+c+d+e=0 and e-a=3
The max value of e can be 2, and then a will be -1, but then there will be atleast TWO -1 to cancel out 2.. hence mode will not be positive..
Only other option is when e is 1, then a=-2......-2, -1, 1, 1, 1
So 1 will be the median

C
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The average of set S comprising 5 non-zero integers is 0. What is its 01 Oct 2019, 04:46
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chetan2u
Archit3110
Asad
The average of set S comprising 5 non-zero integers is 0. What is its median?
1) The range of set S is 3
2) Set S has a unique mode that is positive


I am not able to figure out what would be the set value which satisfies both the given statement

The set can be many as the digits need not be distinct, so -2, -1, 1,1,1...

The average of set S comprising 5 non-zero integers is 0. What is its median?

1) The range of set S is 3
It could be .. -1, -1, 0, 0, 2 or -2, -1, 1, 1, 1..

2) Set S has a unique mode that is positive
-5, 1, 1, 1, 2 or -4, 1, 1, 1, 1

Combined..
If the numbers are in ascending order a, b, c, d, e.....a+b+c+d+e=0 and e-a=3
The max value of e can be 2, and then a will be -1, but then there will be atleast TWO -1 to cancel out 2.. hence mode will not be positive..
Only other option is when e is 1, then a=-2......-2, -1, 1, 1, 1
So 1 will be the median

C
In the premise, it defines the integers are NON-zero.
So considering statement 1: we have 2 possibilities, -2,-1,1,1,1 and 2,1,-1,-1-1.
considering both statement 1and 2: we only have 1 possibility.
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The average of set S comprising 5 non-zero integers is 0. What is its 01 Oct 2019, 06:03
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Took me 2:47s to do it. Appears to be a 700 level question. Any case, good one.
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The average of set S comprising 5 non-zero integers is 0. What is its 05 Oct 2019, 06:56
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Bunuel, How can we consider elements of a set to be identical? Isn't it against the definition of set? Have seen quite a few solutions on similar lines.
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The average of set S comprising 5 non-zero integers is 0. What is its 14 Oct 2019, 08:00
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Archit3110
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The average of set S comprising 5 non-zero integers is 0. What is its median?
1) The range of set S is 3
2) Set S has a unique mode that is positive


#1
The range of set S is 3
-2,-1,1,1,1
2,1,-1,-1,-1
insufficient
#2
Set S has a unique mode that is positive
it can be any set value with mode of +ve value insufficient
from 1 &2
only possible set value -2,-1,1,1,1
median ; 1
IMO C

@ @Archit3110 How did you consider identical elements within a set? Isn't it against the very definition of a set?
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The average of set S comprising 5 non-zero integers is 0. What is its 14 Oct 2019, 08:28
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Q. The average of set S comprising 5 non-zero integers is 0. What is its median?

1) The range of set S is 3
The set could be {-2, -1, 1, 1, 1} or {-1, -1, -1, 1, 2}. That means median can be 1 or -1.
Insufficient

2) Set S has a unique mode that is positive
The set could be {-2, -1, 1, 1, 1}, {-3, -3, 2, 2, 2}, {-6, -6, 4, 4, 4}, etc. That means median can be 1, 2, 4, etc.
Insufficient

1) and 2)
We can narrow down that the only possible set should be {-2, -1, 1, 1, 1}
sufficient

Final Answer is (C)
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