Question:

There are 7 numbers in the set and all the numbers are distinct integers. What is the median of these 7 numbers, when they are arranged in an ascending order?

(1) Median of the first five numbers is 11

(2) Median of the last five numbers is 13

Option Choices:

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.

B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient.

C. Both statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

D. Each statement ALONE is sufficient.

E. Statement (1) and (2) TOGETHER are not sufficient.

To properly assess your DS skills, try to solve the question on your own before scrolling down to the solution. You can find the correct answer at the end of the solution.

Solution :

Step 1: Analyse Question Stem

  • It’s given that all the numbers are distinct integers
  • We need to find, what is the median of the 7 numbers, when all of them are arrange in an ascending order.
    • Let’s assume the numbers as N1, N2, N3, N4, N5, N6, and N7
      • Where N1 < N2 < N3 < N4 < N5 < N6 < N7
      • The median in this case is N4.

Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE

Statement 1: Median of first five numbers is 11

N1  
N2  
N3 11
N4  
N5  
N6  
N7  

Here the median of 7 numbers is N4 but we can’t infer anything about N4 from this statement.

Hence, statement 1 alone is not sufficient. We can eliminate answer option A and D.

Statement 2: Median of last five numbers is 5

N1  
N2  
N3  
N4  
N5 13
N6  
N7  

Here also we cannot infer anything about number N4.

Hence, statement 2 also not sufficient. We can eliminate option B

Step 3: Analyse Statements by Combining

From statement 1:

N3 = 11

Frome statement 2:

N5=13

After combining the 2, we get 

N1  
N2  
N3 11
N4  
N5 13
N6  
N7  

Since, all the numbers are distinct integers and arranged in ascending order, N4 must be 12.

Thus, the median is 12 and the correct answer is option C