Q. Five friends – Gaurav, Himanshu, Ishan, Lokesh, and Mukul – are of different ages. Who is the third oldest?
(I) Ishan is older than Gaurav but younger than Lokesh.
(II) Mukul is older than Ishan but younger than Lokesh.
Solution: Data Sufficiency for Age Puzzle
The question asks to identify the third oldest among five friends: Gaurav (G), Himanshu (H), Ishan (I), Lokesh (L), and Mukul (M), who are all of different ages.
Statement I Analysis
Statement I says: "Ishan is older than Gaurav but younger than Lokesh."
This establishes the following age order:
$Lokesh > Ishan > Gaurav$
This inequality only involves three friends (L, I, G). The positions of Himanshu (H) and Mukul (M) are unknown. Therefore, Statement I alone is not sufficient to determine the third oldest friend.
Statement II Analysis
Statement II says: "Mukul is older than Ishan but younger than Lokesh."
This establishes the following age order:
$Lokesh > Mukul > Ishan$
This inequality also involves only three friends (L, M, I). The positions of Gaurav (G) and Himanshu (H) are unknown relative to these three and each other. Therefore, Statement II alone is not sufficient to determine the third oldest friend.
Combined Statements Analysis
Combining both statements:
- From Statement I: $L > I > G$
- From Statement II: $L > M > I$
Combining these gives us a partial order:
$Lokesh > Mukul > Ishan > Gaurav$
This accounts for four friends (L, M, I, G). However, the fifth friend, Himanshu (H), is not mentioned in either statement. His age relative to the others is unknown.
Himanshu could be the oldest, second oldest, third oldest, fourth oldest, or youngest. Consider these possibilities for the complete order:
- H > L > M > I > G (Third oldest: M)
- L > H > M > I > G (Third oldest: M)
- L > M > H > I > G (Third oldest: H)
- L > M > I > H > G (Third oldest: I)
- L > M > I > G > H (Third oldest: I)
Since the third oldest person could be Mukul (M), Himanshu (H), or Ishan (I) depending on Himanshu's exact age, the data in both statements together is insufficient to answer the question.
Conclusion
The data provided in both Statement I and Statement II together are not sufficient to determine who the third oldest friend is.
Important Questions from Data Sufficiency
Consider two Statements and a Question:
Statement 1: Priya is 4 ranks below Seema and is 31 st from the bottom.
Statement 2: Ena is 2 ranks above Seema and is 37" from the bottom.
Question: What is Seema’s rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question:
Statement 1: Each of A and D is heavier than each of B, E and F, but none of them is the-heaviest.
Statement 2: A is heavier than D, but is lighter than C.
Question: Who is the heaviest among A,B,C, D and E?
Which one of the following is correct in respect of the Statements and the Question ?
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Consider the Question and two Statements given below :
Question : Is xan integer?
Statement-1 : x / 3 is not an integer.
Statement-2 : 3 xis an integer.
Which one of the following is correct in respect of the Question and the Statements?
Consider the Question and two Statements given below:
Question : What is the age of Manisha?
Statement-1: Manisha is 24 years younger than her mother.
Statement-2 : 5 years later, the ages of Manisha and her mother will be in the ratio 3 : 5.
Which one of the following is correct in respect of the Question and the Statements?
