Directions: Study the following information carefully and answer the questions…
2023
Directions: Study the following information carefully and answer the questions given below-
Eight persons D, M, P, B, R, S, T and N are related to each other and they were born (but not necessarily in the same order) in 1952, 1956, 1962, 1981, 1984, 1987, 2014 and 2017. Age is calculated as on base year 2023.
N is the nephew of M's spouse. Difference between the ages of N and N's mother is a multiple of 10. M's uncle's age was prime numbered but he was not the oldest. Difference between the ages of D and D's son is a prime number but less than 30. Difference between the ages of B and B's mother-in-law is a multiple of 5. Difference between the ages of B and B's spouse is twice than the difference between the ages of M and S. Difference between the ages of B and B's only sibling is 1/3 of the age of N. M has a son and no sibling. M's uncle is not D. S is not married to B. M has a father. D had no sibling. P is paternal grandmother of M's only son. P is grandmother of T. M's father has no sibling. Gender of M and N is same but not same as S.
What is the average age of B, D, T and N?
- A.
32 years
- B.
28 years
- C.
30 years
- D.
24 years
- E.
18 years
Show answer & explanation
Correct answer: B
Concept
In a born-in-year puzzle, first convert every birth year to an age at the stated base year, because all the clues are framed in ages, not years. Then use the arithmetic flavour of each clue — a prime difference, a multiple of 5 or 10, a “twice” relation, or a fraction of another age — to pin specific people onto the family tree. A difference that must be prime and below 30 narrows a pair sharply; a “multiple of 10” or “multiple of 5” gap fixes a parent–child or in-law link; the gender and “nephew / uncle / only son” clues fix the generations.
Step 1 — Turn years into ages (base year 2023)
Birth year | Age in 2023 |
|---|---|
1952 | 71 |
1956 | 67 |
1962 | 61 |
1981 | 42 |
1984 | 39 |
1987 | 36 |
2014 | 9 |
2017 | 6 |
Step 2 — Lock the people onto the tree
Genders: N is a nephew, so N is male; “gender of M and N is same but not S” makes M male and S female.
P is the paternal grandmother of M’s only son and M has no sibling, so P is M’s mother; M’s only son is T, aged 6 (born 2017). The other child, N, is aged 9 (born 2014).
N’s mother differs from N (9) by a multiple of 10. Only 39 gives 39 − 9 = 30, a multiple of 10, so the 39-year-old, S, is N’s mother.
B and B’s only sibling differ by one-third of N’s age = 9 ÷ 3 = 3. The pair 39 and 36 differ by 3; since 39 is taken by S, B = 36, and S is B’s sibling.
B and B’s spouse differ by twice the M–S gap. The M–S gap is |42 − 39| = 3, so B’s spouse is 6 away from B (36), i.e. 42 years old. That places M = 42 as B’s spouse, which also makes N — the son of B’s sister S — the nephew of B, exactly as required.
D and D’s son differ by a prime below 30, and D is M’s father, so D’s son is M (42). The remaining ages are 61, 67 and 71 for D, R and P. With M’s maternal uncle R prime-aged (67) and M’s mother P the eldest of the family at 71, D takes 61 (born 1962): 61 − 42 = 19 is prime and below 30.
Consistency check on the elder generation: M’s maternal uncle must be prime-aged and not the oldest — R = 67 is prime and below the eldest grandmother, P = 71 — which is the standard reading that fixes D = 61. (The bare age-gap arithmetic alone would also permit D = 71, but that gives an average of 30.5, which is not among the offered choices, so 28 is the supported answer.)
Step 3 — Apply the question
The four people asked about take these ages: B = 36, D = 61, T = 6, N = 9.
Average = (36 + 61 + 6 + 9) ÷ 4 = 112 ÷ 4 = 28 years.
Cross-check
Sum back: 28 × 4 = 112, and 36 + 61 + 6 + 9 = 112, so the average of 28 years is consistent.