Directions: Study the following information carefully and answer the questions…

Concept

In a blood-relation + age puzzle, convert each birth year to an age with the stated base year, then turn every kinship clue into a numeric condition (a difference that is a multiple, a prime, or a fraction of another age). "B's mother-in-law" is the mother of B's spouse, so the task is to fix who B's spouse is and then that spouse's mother.

Application — pin the ages step by step

1. N's age: the difference between N and N's mother is a multiple of 10, and the B-sibling clue (difference = N ÷ 3) needs N divisible by 3. Two year-pairs are a multiple of 10: N = 9 (2014) with mother 39 (1984), and N = 6 (2017) with mother 36 (1987) — both have N divisible by 3. The pair N = 6 fails later, because N ÷ 3 = 2 and no two available ages differ by 2, leaving no valid B-sibling pair. So N = 9 and N's mother = 39.

2. B and B's only sibling differ by N ÷ 3 = 3. Age pairs differing by 3 are (42, 39) and (39, 36); both use 39 (N's mother). Test each: if B = 42 then the rest forces M = 36, but then M's father would need an age difference from M that is prime and < 30 with only 71 left for the father (71 − 36 = 35, not prime) — that branch collapses. So B = 36, with B's sibling = 39. Hence N's mother (39) is B's sibling.

3. Because N is the nephew of M's spouse, M's spouse is a sibling of N's mother (39). B is the only sibling of 39, so B is M's spouse; M is then the remaining middle-aged value, M = 42.

4. Spouse check: difference between B and B's spouse (M) = 42 − 36 = 6 = twice the difference between M and S (S = 39): 2 × (42 − 39) = 6. Consistent.

5. M's only son is the remaining child age, 6 (T), and P is his paternal grandmother, so P = M's mother. P is therefore the mother of B's spouse M.

6. The three elders are 71, 67, 61 (all prime). M's father has no sibling, so M's uncle is on the mother's side (mother's brother). The uncle is prime but not the oldest, so the uncle = 67. M's father (D) needs |father − M| prime and < 30; with M = 42 this leaves the mother and father as 71 and 61 in some order.

D and P (M's father and mother) take the remaining two ages, 71 and 61, in an order that the bare clues alone cannot fix — resolved next using the offered options.

Why the answer is 71 among the given choices

Both 71 − 42 = 29 and 61 − 42 = 19 are prime and below 30, so the bare clues allow M's mother (and hence B's mother-in-law) to be either 71 or 61. The choices, however, offer 71 but not 61, so the only value that can be B's mother-in-law among the options is 71. The numeric in-law check confirms it: 71 − 36 = 35 is a multiple of 5, as required between B and B's mother-in-law.

Cross-check

• Difference between B (36) and the answer (71) = 35, a multiple of 5 — satisfied.

• Given 71 is fixed as B's mother-in-law (M's mother) from the offered options, the remaining elder value falls to M's father (61), while 67 is M's maternal uncle (fixed independently in the derivation); neither 61 nor 67 is the mother of B's spouse.

• Among the offered ages, 6 (M's son), 39 (B's sibling), 9 (N, the nephew) and 67 (M's uncle) each name the wrong relative; only 71 reaches the mother of B's spouse.