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
Which of the following statement is correct?
I. The value of 1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ...... + 222 - 212 is 4840.
II. The value of
\(\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right) \) \(\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)\) is \(k^{16}- \frac{1}{k^{16}}\).
Given below is a question followed by two statements I and II. Read both statements carefully to decide which one of them is sufficient to answer the question.
Six people - A, B, C, D, E and F are sitting in a straight line facing north. Who sits to the immediate left of D?
(I) A sits second from one of the extreme ends of the line. Only two people sit between A and B. E sits to the immediate right of C.
(II) C sits third from the left end of the line. Only one person sits between C and F. E sits third to the right of F.
Please read the below equation and select an appropriate option from the following.
x + y = 10 ; y = x - 2
Quantity A is x.
Quantity B is y.
A lady wants to buy the following items in the given price range-
1. Tomato between Rs. 40 and Rs. 45 per kg.
2. Grapes in the price range of Rs. 80 and Rs. 90 per kg.
3. Milk packets at Rs. 23 per liter.
In which shop from the following will she definitely get all her items/
A. Shop S sells tomato at Rs. 22.5 per half kg, Grapes at Rs. 82 per kg and milk at Rs. 24 per liter.
B. Shop H sells grapes at Rs. 21 per quarter kg, milk at 12.5 per half litre and tomato at Rs. 22 per half kg.
C. Shop O sells milk at Rs. 11.5 per half litre, tomato at 21 per half kg and grapes at Rs. 43 per half kg.
D. Shop P sells tomato at Rs. 23.5 per half kg, grapes at Rs. 85 per kg and milk at Rs. 23 per litre.You are given a question and two statements. Identify which of the statements is/are sufficient to answer the question.
Question:
When is Yuvi's wedding anniversary?
Statements:
1: On the 7 th day of a month.
2. The month has 29 days only in a leap year.
