Directions : Study the following information carefully to answer the given…
2022
Directions : Study the following information carefully to answer the given questions:
9 persons P, Q, R, S, T, U, V, W and X of different age belong to three different states viz. Assam, Manipur and Tripura but not necessarily in the same order. Not less than two and not more than four persons belong to any state.
Note: If it is given that A and the one who is 12 years old belong to same state then it means A is not 12 years old.
W and the one who is 51 years old belong to same state. Only Q and the one whose age is 18 years belong to same state. P and V belong to different state. W is 7 years younger to V. S is twice older to Q. P and S belong to different state. V who is 61 years old and the one whose age is 64 years belong to same state. S neither belongs to Assam nor Tripura. The one whose age is 35 years belong to Tripura. No one’s age is less than 18 years and more than 68 years. T and the one who is 64 years old belong to the same state. W does not belong to Tripura. U and the one who is 29 years old belong to same state. P is not belonged to Assam. R is 29 years old and 3 years younger to Q. X is the youngest one. P is 2 years older to U. P’s age is not multiple of 5.
Who among the following belongs to Manipur?
- A.
The one who is 37 years old
- B.
U
- C.
The youngest one
- D.
T
- E.
Both T and U
Attempted by 3 students.
Show answer & explanation
Correct answer: D
Concept
This is a state-grouping puzzle. The strategy is to first fix every person's AGE from the numeric clues (all ages are distinct), and only then place each person into a state using the 'same-state' and 'different-state' links. A key device is the negative-implication note: 'A and the one who is N years old belong to the same state' means A is a different person from the N-year-old, so A is NOT N years old.
Step 1 - Fix the ages
R is 29, and R is 3 years younger than Q, so Q = 29 + 3 = 32.
S is twice Q, so S = 2 x 32 = 64. This is the person who is 64 years old.
V is 61, and W is 7 years younger than V, so W = 61 - 7 = 54.
The remaining people P, T, U, X must carry the still-referenced ages 51, 35 and 18 (the ages 29, 32, 64, 61, 54 are already taken and all ages are distinct).
X is the youngest of all nine, so X = 18 (the smallest permitted age).
P = U + 2 and P is not a multiple of 5. Taking U = 35 gives P = 37 (not a multiple of 5), leaving T = 51. The alternatives (U = 51 forcing P = 53, or U = 49) cannot leave 35 and 18 placeable as distinct, in-range ages with the youngest = 18, so they are rejected.
Final ages: P 37, Q 32, R 29, S 64, T 51, U 35, V 61, W 54, X 18.
Step 2 - Place into states
S is neither Assam nor Tripura, so S (64) is in Manipur.
V (61) shares a state with the 64-year-old (S), so V is in Manipur; T also shares a state with the 64-year-old, so T (51) is in Manipur.
W shares a state with the 51-year-old (T), so W (54) is in Manipur. Manipur now holds S, T, V, W (its maximum of 4).
'Only Q and the 18-year-old (X) belong to the same state' fixes a state of exactly two people: Q (32) with X (18).
The 35-year-old (U) is in Tripura; R (29) shares U's state, so R is in Tripura; P is not Assam and must differ from V and S (Manipur), so P is in Tripura too.
That leaves Q and X as the only remaining pair, forming the exactly-two state Assam.
State | Members (age) |
|---|---|
Manipur | S 64, T 51, V 61, W 54 |
Tripura | P 37, U 35, R 29 |
Assam | Q 32, X 18 |
Step 3 - Answer the question
The question asks who belongs to Manipur. Manipur = {S, T, V, W}. Among the offered choices, T is the only person who lies in Manipur, so the answer is T.
Cross-check
All state sizes are 2, 3 and 4 (within the 2-to-4 limit, summing to 9). P (Tripura) differs from V and S (Manipur); W is not in Tripura; the 35-year-old is in Tripura; Q's state holds exactly Q and the 18-year-old. Every clue is satisfied, confirming Manipur = S, T, V, W.