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. What is the sum of the age of E and K?

### 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:** * Based on our mapping, the age of E is 42 years. * The age of K is 39 years. * The sum of their ages is $$42 + 39 = 81$$ years. ### 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 mistake is attempting to solve the family tree and ages independently. They must be solved simultaneously, as clues like "C's son" directly constrain which ages can be assigned to C (Gen 1) and E (Gen 2). ### Final Answer Therefore, the correct answer is **81 years**.