A set of 51 different integers has a median of 30 and a range of 60.

Question

A set of 51 different integers has a median of 30 and a range of 60. What is the value of the least possible integer in this set?

A. -10
B. -6
C. -5
D. 5
E. 10

To solve question 4:    Question 4

To read the article:      Solve any Median and Range question in a minute

Nikhil · Accepted Answer

To find the least possible integer in the set of 51 different integers

The median of the set is 30

=> If the numbers are arranged in ascending order, the 26th integer is 30

We know that all the integers to the right of the median are  \geq  median.

Since the set consists of all different integers, the integers to the right of the median are  >  median

Lets make the integers to the right of the median greater than median by least possible value i.e 1

=> value at 27th place will be 31(27+4)
=> value at 28th place will be 32(28+4)
...... => value at 51st place will be 55(51+4)

Given range = 60

=> max_possible_integer - lowest_possible_integer = 60

=> 55 - lowest_possible_integer = 60

=> lowest_possible_integer = 55 - 60 = -5

Hence  option C

PKN · Answer

Given set, Say
X={ x_{min} ,.....(25 members including  x_{min} )......, 30 ,.......(25 members including  x_{max} )....., x_{max} } 
---------------------------------------------------(26th term  Median ) ---------------------------------  (51^{th} term) 
Given,  x_{max} - x_{min}=60  ----(1)
Since number of members after median is 25, hence x(max)=30+25=55 (Note:- all terms of the set are different as given)
So, substituting in (1), we have
  55-x_{min}=60 
Or,  x_{min}=-5

Therefore, the value of the least possible integer in this set is -5.

Ans. (C)

anantdixit · Answer

Median is 30...thus there are 25 digits above 30...the smallest number 25 digits above 30 is 55.....the range is 60....therefore the smallest number possible has to be -5...option c for me

vaibhav1221 · Answer

median is 30 which is the 26th number in the series.
In order to minimize the lowest number, we need to minimize the maximum number.
Because,
(X)(smallest highest number) - (Y)(least negative number) = 60 (to minimize Y)

the smallest highest number possible for this series is 55. Because  30+25 = 55 . 25 different integers ahead of the median.

Therefore,

55 - x = 60 
 x=-5

EgmatQuantExpert · Answer

Solution

Given:  
• 51 different integers have a median 30 and range 60.

To find:  
• The value of least possible integer.

Approach and Working:   
We will get the value of least possible integer if then the highest element of the set is equal to the median.
However, all the elements of the set are different.
So, highest element must be as small as possible.
Now, we know, median will be 51+1/2=1= 26 element.
• Hence, minimum value of the highest element= 30+25= 55
• Thus, highest element – lowest element= 60
o 55- Lowest element= 60
o Lowest element= -5

Hence, the correct answer is option C.

Answer: C

exc4libur · Answer

num of terms=51 (different integers)
median=26th.term=30
range=51st-1st.term=tn-a=60… a=tn-60

tn must be larger than the median and the following 24 terms (since they are all different)
tn>30+24>54
a=tn-60…a>54-60…a>-6

Answer (C).

firas92 · Answer

The median of a set of 51 elements is the 26th element.

So we have 25 elements after the median.

When we take one of the answer choices and workout the largest element, we need to see if the largest element is at least 25 integers away from 30 so as to get distinct elements.

(A) -10
 In this case, the largest element is 50 which is only 20 integers away from 30 - Eliminate

(B) -6
 In this case, the largest element is 54 which is only 24 integers away from 30 - Eliminate

(C) -5
 In this case, the largest element is 55 which is 25 integers away from 30 - Correct

Answer is  (C)

ScottTargetTestPrep · Answer

Solution:

Since 30 is the median of the 51 distinct integers, there must be 25 integers greater than 30 and another 25 integers less than 30. Thus, the smallest possible value of the largest integer is 30 + 25 = 55. Since the range is 60, the least possible integer is 55 - 60 = -5.

Answer: C

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A set of 51 different integers has a median of 30 and a range of 60.

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A set of 51 different integers has a median of 30 and a range of 60.

Prep Toolkit

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