Read the given information carefully and answer the question that follows.…
2024
Read the given information carefully and answer the question that follows.
Seven persons were born on the same date and in the same month but in different years - 1955, 1967, 1973, 1980, 1987, 1991 and 2003. Consider the base year 2024 to calculate the ages.
L's age is a multiple of 3. Three persons were born between L and Q. The number of persons born before Q is the same as the number of persons born after P. The difference between the ages of Q and K is 12 years. M is 7 years older than N. N is younger than O.
If P is related to L and N is related to Q, then M is related to ___.
- A.
K
- B.
O
- C.
L
- D.
None of these
- E.
N
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept
In an ordered-arrangement puzzle, first fix the linear order of all elements from the numeric data (here, birth years give an oldest-to-youngest order). Then translate each clue into a position or a gap inside that single order, and use the clues together to eliminate every layout except one. Finally, a "X is related to Y" mapping is a hidden positional rule: read the constant gap from the given pairs, then apply that same gap to the asked element.
Step-by-step arrangement
Base year 2024, so age = 2024 - (birth year). Number the seven slots 1 to 7 from oldest to youngest; the ages in that order are 69, 57, 51, 44, 37, 33, 21.
L's age is a multiple of 3. Among the ages, only 69, 57, 51, 33 and 21 are multiples of 3 (44 and 37 are not), so L cannot sit in slot 4 or slot 5.
"Persons born before Q" equals "persons born after P". If Q is in slot q and P in slot p, this says (q - 1) = (7 - p), i.e. p + q = 8. (This does not yet pin them to the ends - any pair of slots summing to 8 qualifies.)
Three persons are born between L and Q, so the slots of L and Q differ by 4. Combining p + q = 8 with |L - Q| = 4 leaves only these (P, Q, L) slot triples: (1, 7, 3), (3, 5, 1) and (5, 3, 7); the case (7, 1, 5) is rejected because slot 5 has age 37, which is not a multiple of 3, and L must be a multiple of 3.
The age difference of Q and K is 12. Test the three surviving triples: only (P, Q, L) = (1, 7, 3) leaves a person exactly 12 years from Q (Q is 21, so K is 33); in the other two triples no remaining person is 12 years from Q. So P is oldest (slot 1, 1955) and Q youngest (slot 7, 2003), with L in slot 3 (1973, age 51) and K in slot 6 (1991, age 33).
M is 7 years older than N, i.e. age(M) = age(N) + 7; among the remaining slots only 44 and 37 differ by 7, so M is 44 (1980) and N is 37 (1987). N is younger than O, leaving O = 1967 (age 57).
The complete oldest-to-youngest order is therefore:
Slot (oldest first) | Person | Birth year | Age in 2024 |
|---|---|---|---|
1 | P | 1955 | 69 |
2 | O | 1967 | 57 |
3 | L | 1973 | 51 |
4 | M | 1980 | 44 |
5 | N | 1987 | 37 |
6 | K | 1991 | 33 |
7 | Q | 2003 | 21 |
Finding the relationship rule
Read the given pairs as slots in this order. P (slot 1) is related to L (slot 3); N (slot 5) is related to Q (slot 7). In both pairs the related person sits two slots toward the younger end. So the hidden rule is: each person is related to the person two slots younger.
Apply to M
M sits in slot 4. Two slots toward the younger end is slot 6, occupied by the person aged 33 (born 1991), namely K. Hence M is related to K.
Cross-check
Both given mappings (1->3 and 5->7) jump exactly two slots, and 4->6 also jumps exactly two slots, so the gap and direction match. The mapping is consistent, confirming the related person is K.