Direction: Read the following information carefully and answer the given questions. Eight students A, C, E, F, G, H, K, and L are related to each other born in 1953, 1957, 1963, 1982, 1985, 1988, 2015, and 2018 not necessarily in the same order. Age is calculated from 2024. E's spouse has a niece who is F. The difference between F and F's mother's age is a multiple of 10. The difference between A and A's mother-in-law's age is a multiple of five. E's uncle's age was prime but he was not the eldest. The difference between C and C's son is a prime number less than twenty. The difference between E and E's spouse's age is double the difference between the E and K age. A has a sibling only. E has a son. E's uncle is not C but E's uncle's age is a prime number. K is not married to A. E has a father. There is an equal number of males and females. C has no siblings. G is the grandmother of E's only son. G is the grandmother of L. E's father has no sibling of his own and E's mother has no sister. How is K related to F?

### Concept & Blood Relation and Age Puzzle This puzzle requires parallel solving of a family tree and an age-to-person mapping. First, calculate all absolute ages from the base year 2024. Then, use gender counts (4 males, 4 females) and generation gaps to lock in the family structure before assigning specific ages based on mathematical constraints. ### Step-by-Step Solution **1. Age Calculation (Base Year 2024):** * $$2024 - 1953 = 71$$ years * $$2024 - 1957 = 67$$ years * $$2024 - 1963 = 61$$ years * $$2024 - 1982 = 42$$ years * $$2024 - 1985 = 39$$ years * $$2024 - 1988 = 36$$ years * $$2024 - 2015 = 9$$ years * $$2024 - 2018 = 6$$ years **2. Decoding the Family Tree:** * "G is the grandmother of E's only son" and "G is the grandmother of L": E is married and has a son L. G is the mother of E or E's spouse. * "E's father has no sibling... E's mother has no sister" but "E's uncle's age was prime": This means E's mother MUST have a brother (who is E's uncle). Thus, G is E's mother, and G has a brother. Let's identify the father as C (since "C has no siblings"). * "A has a sibling only" & "E's spouse has a niece F": Let A be E's spouse. A's only sibling is K. Since F is A's niece, F is the daughter of K. * Checking genders for 4M/4F balance: C(M), Uncle H(M), E(M), L(M) makes 4 Males. G(F), A(F), K(F), F(F) makes 4 Females. This fits perfectly. **3. Mapping Ages:** * "Uncle's age was prime but he was not eldest": Primes are 61, 67, 71. Eldest is 71. Uncle H is either 61 or 67. * "Diff between C and C's son (E) is a prime < 20": If C = 61 and E = 42, diff is 19 (a prime < 20). Thus C = 61, E = 42. This leaves Uncle H = 67 and Grandmother G = 71. * "Diff between A and A's mother-in-law (G) is a multiple of 5": G = 71. A must be 36 since $$71 - 36 = 35$$. * Since K is A's sibling in the same generation, K = 39. * "Diff between F and F's mother's (K=39) age is a multiple of 10": F must be 9 since $$39 - 9 = 30$$. * This leaves L = 6. **4. Answering the Specific Question:** * From our family tree derivation, we established that A is E's spouse, and K is A's only sibling. * Since F is the niece of A, and K is A's only sibling, F must logically be the daughter of K. * Furthermore, we established K is a female (to maintain the 4M/4F gender balance). * Therefore, K is the mother of F. ### Exam Strategy & Shortcut Always translate birth years to absolute ages immediately. It transforms vague chronological statements into strict mathematical conditions. Find the generation boundaries first (Grandparents > 60, Parents ~ 30-45, Kids < 15) to drastically reduce trial-and-error combinations. ### Common Pitfall A common pitfall is forgetting to strictly enforce the "equal number of males and females" rule, which is the only way to lock down K's gender as female instead of male in this puzzle. ### Final Answer Therefore, the correct answer is **Mother**.