M43-05

Question

\{a_1, \ a_2, \ a_3, \ ..., \ a_n\} 
 
In the list of  n  numbers, where  n > 4 , shown above  a_1 < a_2 < a_3 < ... < a_{n} . Each of the following could change the median of the list EXCEPT:

A. Dividing  a_n  by 2
B. Taking the square root of  a_1 
C. Squaring  a_n 
D. Doubling  a_n 
E. Increasing  a_n  by 20

Bunuel · Answer

Official Solution:

\{a_1, \ a_2, \ a_3, \ ..., \ a_n\} 
 
In the list of  n  numbers, where  n > 4 , shown above  a_1 < a_2 < a_3 < ... < a_{n} . Each of the following could change the median of the list EXCEPT:

A. Dividing  a_n  by 2
B. Taking the square root of  a_1 
C. Squaring  a_n 
D. Doubling  a_n 
E. Increasing  a_n  by 20

The median of a list of values is the middle value for an odd number of values and the average of the two middle values for an even number of values, that is when the values are arranged in order. Thus, the question essentially asks for an option that cannot possibly change the order of the values in the list.
 
Given list:  \{a_1, \ a_2, \ a_3, \ ..., \ a_n\} , where  a_1 < a_2 < a_3 < ... < a_{n} .
 
A. Dividing  a_n by 2
 
This operation could change the order of the values. Example:
 
Consider the list {1, 2, 3, 4, 5}. The median is 3.
 
Dividing  a_n  (5) by 2, the new list is {1, 2, 3, 4, 2.5}. The new sorted list is {1, 2, 2.5, 3, 4}. The new median is 2.5.
 
The median has changed.
 
B. Taking the square root of  a_1 
 
This operation could change the order of the values. Example:
 
Consider the list {0.25, 0.3, 0.35, 0.4, 0.45}. The median is 0.35.
 
Taking the square root of  a_1  (0.25), the new list is {0.5, 0.3, 0.35, 0.4, 0.45}. The new sorted list is {0.3, 0.35, 0.4, 0.45, 0.5}. The new median is 0.4.
 
The median has changed.
 
C. Squaring  a_n 
 
This operation could change the order of the values. Example:
 
Consider the list {0.1, 0.2, 0.3, 0.4, 0.5}. The median is 0.3.
 
Squaring  a_n  (0.5), the new list is {0.1, 0.2, 0.3, 0.4, 0.25}. The new sorted list is {0.1, 0.2, 0.25, 0.3, 0.4}. The new median is 0.25.
 
The median has changed.
 
D. Doubling  a_n 
 
This operation could change the order of the values. Example:
 
Consider the list {-1.4, -1.3, -1.2, -1.1, -1}. The median is -1.2.
 
Doubling  a_n  (-1), the new list is {-1.4, -1.3, -1.2, -1.1, -2}. The new sorted list is {-2, -1.4, -1.3, -1.2, -1.1}. The new median is -1.3.
 
The median has changed.
 
E. Increasing  a_n  by 20
 
This operation will increase the largest term by 20, hence whatever  a_n  was, its value will increase, and the order of the elements would still remain the same:  a_1 < a_2 < a_3 < ... < a_{n} .

Answer: E

sakshamsri95 · Answer

I think this is a  high-quality  question and I agree with explanation.

adityamntr · Answer

I don’t quite agree with the solution. This question has 2 problems -  
 1. value of median will still change with option 5. This is a very bad representation for a gmat qaunt question.The value of n won;t change but n is not median , median is an whose value will change

Bunuel · Answer

You should read the question and solution more carefully. The question is correct, it asks which option cannot  change the median . In option E, increasing the largest value does not affect the order, so the middle element(s) stay the same. The median value does  not  change. Learn the difference between changing a value and changing the median.

adityamntr · Answer

Understood it now! I misunderstood that A(n) was representing each element of the list (where n is variable from 1,2,3... ) rather than just the last one. All of it makes sense now. My bad, I couldn't decipher it and blamed it on the ques.

starblazer65 · Answer

I like the solution - it’s helpful.

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