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

Question

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

niks18 · Accepted Answer

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

sobby · Answer

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 ..

Sasindran · Answer

IMO D.

Here median is asked. 
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

pushkarajnjadhav · 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.
Answer should be D. 
22-(-38)=60
-38,........., 15(median), 16, 17,18,19,20,21,22

sudha8050 · Answer

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

niks18 · Answer

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

KS15 · Answer

C cant be the answer. Answer is D. We need 15 different integers-so 15 cant be the greatest number.

GMATYoda · Answer

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.

vivapopo · Answer

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
SO D IS ANSWER COZ:
8, 9, 10,11,12,13,14, 15(median), 16, 17,18,19,20,21,22

newyork2012 · Answer

gaga different numbers ..

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

22-x=60 x=-38

ScottTargetTestPrep · Answer

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.

Answer: D

Aamirso · Answer

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.

C is my answer.

cartiro · Answer

Hi, 
I understand that A,B and C cannot be the least value. However, can someone further explain why is it D and not E??

Range= Max - Min // Min= Max - Range

A.Can´t be because the maximum would then be 0, which is smaller than the median 
B. Can´t be either because the maximum would be 12, which is smaller than the median
C. Can´t be either because the maximum would be 15, and it says that all numbers should be different.
But, 
D. Could be an option, because the maximum (-38+60= 22). Thus, 22 is different and greater than 15. ok
E. But this one could also be an answer (-32+60= 28). Thus, 28 is different and greater than 15 too.

The numbers are not consecutive, so why E is not an option??

Thanks!

niks18 · Answer

Hi,

The question asks smallest value and -38 is smaller than -32

Posted from my mobile device

LeenaSai · Answer

Why you are increasing the numbers after the median one by one ?

Posted from my mobile device

LeenaSai · Answer

Hi there ,

I couldn’t understand the fact that the numbers after the median are taken in series , 16,17,18,19,20,21,22 ??

Why is it so ?

Why we can’t take random numbers after the median ?

Kindly guide

Posted from my mobile device

niks18 · Answer

Hi  LeenaSai

All the numbers have to be different and the question asks for smallest possible value, hence the difference between all the numbers have to be as small as possible. As all are integers, the smallest difference between two different integer has to be 1. If you pick random numbers, the you will not get smallest value...Try with some numbers to understand

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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

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