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# Set J consists of 15 different integers. If the median of Set J is 15

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Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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11 Nov 2017, 05:16
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Question Stats:

52% (01:06) correct 48% (01:34) wrong based on 132 sessions

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Set J consists of 15 different integers. If the median of Set J is 15 and the range is 60, what is the smallest possible value contained within Set J?

A. -60
B. -48
C. -45
D. -38
E. -32

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Re: Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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11 Nov 2017, 06:02
Bunuel wrote:
Set J consists of 15 different integers. If the median of Set J is 15 and the range is 60, what is the smallest possible value contained within Set J?

A. -60
B. -48
C. -45
D. -38
E. -32

will go with C ...
The largest number must be greater than or equal to 15..
lets plugin value ...
a. -60 --then if range have to be 60...greatest number will be 0 --( 0-(-60) = 60 range ..but greatest number cannot be less than 15 , so out
b -48 - we will get greatest number as 12 ..so out
C- -45 --we will get greatest number as 15.... (15-(-45)) = 60 ..range ..so our answer ..
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Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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Updated on: 11 Nov 2017, 06:44
1
Bunuel wrote:
Set J consists of 15 different integers. If the median of Set J is 15 and the range is 60, what is the smallest possible value contained within Set J?

A. -60
B. -48
C. -45
D. -38
E. -32

$$Range = Max - Min$$

so $$Min = Max - Range => Min = Max - 60$$

so for $$Min$$ value to be the lowest $$Max$$ value has to be as low as possible. But $$Max$$ value cannot be lower than the median value. and as all numbers have to be different, so $$Max=15+7=22$$ (as all numbers are integer, so to make Max value as low as possible, every number after median has to increase by 1)

$$=> Min = 22-60=-38$$

Option D

Originally posted by niks18 on 11 Nov 2017, 06:13.
Last edited by niks18 on 11 Nov 2017, 06:44, edited 2 times in total.
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Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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11 Nov 2017, 06:29
1
IMO D.

Hence the 8th number is the given median value i.e., 15. and the minimum 15th number is 22.

Range = 22-min.
60=22-min
min=22-60
=-38
Hence D
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Re: Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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11 Nov 2017, 10:22
sobby wrote:
Bunuel wrote:
Set J consists of 15 different integers. If the median of Set J is 15 and the range is 60, what is the smallest possible value contained within Set J?

A. -60
B. -48
C. -45
D. -38
E. -32

will go with C ...
The largest number must be greater than or equal to 15..
lets plugin value ...
a. -60 --then if range have to be 60...greatest number will be 0 --( 0-(-60) = 60 range ..but greatest number cannot be less than 15 , so out
b -48 - we will get greatest number as 12 ..so out
C- -45 --we will get greatest number as 15.... (15-(-45)) = 60 ..range ..so our answer ..

If the largest number in the set is 15 then how can you say that 15 will be a median?
As the given set is a set of distinct number, we can not have 15 as a largest number.
22-(-38)=60
-38,........., 15(median), 16, 17,18,19,20,21,22
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Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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11 Nov 2017, 19:19
Least possible value is Median - range = 15-60 = -45
the lesser the maximum value, the lesser will be the minimum value. We can not lower the maximum value, beyond median, ie.,15.

Ans C
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Re: Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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11 Nov 2017, 20:24
sudha8050 wrote:
Least possible value is Median - range = 15-60 = -45
the lesser the maximum value, the lesser will be the minimum value. We can not lower the maximum value, beyond median, ie.,15.

Ans C

Hi sudha8050

Here you are assuming that the Median, 15 = Maximum value. but its mentioned in the question that all numbers are different. so in my opinion answer should be D
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Re: Set J consists of 15 different integers. If the median of Set J is 15  [#permalink]

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12 Nov 2017, 01:02
sobby wrote:
Bunuel wrote:
Set J consists of 15 different integers. If the median of Set J is 15 and the range is 60, what is the smallest possible value contained within Set J?

A. -60
B. -48
C. -45
D. -38
E. -32

will go with C ...
The largest number must be greater than or equal to 15..
lets plugin value ...
a. -60 --then if range have to be 60...greatest number will be 0 --( 0-(-60) = 60 range ..but greatest number cannot be less than 15 , so out
b -48 - we will get greatest number as 12 ..so out
C- -45 --we will get greatest number as 15.... (15-(-45)) = 60 ..range ..so our answer ..

C cant be the answer. Answer is D. We need 15 different integers-so 15 cant be the greatest number.
Re: Set J consists of 15 different integers. If the median of Set J is 15 &nbs [#permalink] 12 Nov 2017, 01:02
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