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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, 04:16
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75% (hard)

Question Stats:

53% (01:23) correct 47% (01:26) wrong based on 324 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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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, 05:44
5
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, 05:13.
Last edited by niks18 on 11 Nov 2017, 05:44, edited 2 times in total.
##### General Discussion
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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, 05:02
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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11 Nov 2017, 05:29
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, 09:22
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, 18:19
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, 19:24
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, 00:02
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.
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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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06 Oct 2018, 08:48
1
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

In this Min/Max problem, you should recognize that your goal is to come up with the smallest possible value, which means that you want to use as much of the range as possible on the smaller side of the scale.

Since all integers must be different, and the middle value is 15, that means that of the seven values above 15 you want the smallest possible numbers: 16, 17, 18, 19, 20, 21, and 22.

If the largest value is then 22, then you want to go 60 spaces in the opposite direction to use all the range at the low end. Since 22 - 60 = -38, -38 is the answer.
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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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01 Nov 2018, 11:16
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=L-S (LARGEST-SMALLEST)
L>15>S
FROM CHOICES
60-60=0
60-48=12
60-45=15
60-38=22
60-32=28
But we know 15 is MEDIAN SO IT IS THE EIGHTS IN SERIES
8, 9, 10,11,12,13,14, 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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01 Nov 2018, 21:02
gaga different numbers ..

15---16,17,18,19,20,21,22

22-x=60 x=-38
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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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04 Nov 2018, 17:01
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

Since we want to determine the least possible integer in Set J, we want the greatest integer in set J to be as “small” as possible. Since the median is 15, the largest 7 values could be 16, 17, 18, 19, 20, 21, and 22. We see that the largest integer is 22, and, since the range is 60, the smallest integer in the set is 22 - 60 = -38.

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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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22 Nov 2018, 13:05
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

As range is given, the scenario in which the smallest value will have least value is when the highest value has the least value.

If highest value = x, lowest value = x - 60

We need the lowest value of x.

As median is 15, the lowest value of the highest term is also 15 (the case when all values from median onwards are equal).

Hence, lowest value = 15 - 60

= -45.

Re: Set J consists of 15 different integers. If the median of Set J is 15 &nbs [#permalink] 22 Nov 2018, 13:05
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