Read the information carefully and answer the questions given below: Seven…
2025
Read the information carefully and answer the questions given below:
Seven persons A, B, C, D, E, F and G were born on seven different years i.e., 1947, 1959, 1964, 1973, 1978, 1988 and 2001 on the same month and same date. (Base year is considered as 2025 for age calculation). The sum of the ages of C and F is equal to the age of D. G’s age is divisible by 6. The total age of A and G is a prime number. A is just older than F. The sum of the age of B and A is divisible by 5.
What is the age of G?
- A.
37 years
- B.
24 years
- C.
47 years
- D.
52 years
- E.
66 years
Attempted by 1 students.
Show answer & explanation
Correct answer: E
Concept
In a year-of-birth puzzle with a fixed base year, first convert every birth year into an age (age = base year − birth year). Then translate each verbal clue into an arithmetic condition on those ages, and assign the seven ages to the seven persons so that every condition holds at once. Three tools are key: divisibility (a number is divisible by 6 if it is divisible by both 2 and 3), primality (a prime has no divisor other than 1 and itself), and rank order (“just older than” means the very next higher age, with no age in between).
Application
Convert the birth years to ages using base year 2025:
Birth year | Age in 2025 |
|---|---|
1947 | 78 |
1959 | 66 |
1964 | 61 |
1973 | 52 |
1978 | 47 |
1988 | 37 |
2001 | 24 |
So the available ages are 78, 66, 61, 52, 47, 37 and 24. Now apply the clues step by step:
“The sum of the ages of C and F equals the age of D.” Search the age set for a pair that adds up to another available age. 24 + 37 = 61, which is in the set, so C and F take 24 and 37 (in some order) and D = 61. (No other pair of available ages sums to a third available age, so this is forced.)
“A is just older than F.” A must be the very next age above F. If F were 24, the next age up is 37; if F were 37, the next age up is 47. Hold both branches for now.
“The sum of B and A is divisible by 5.” Test the branches: if F = 24 then A = 37, and we would need some remaining age B with (B + 37) a multiple of 5 — the remaining ages 78, 66, 52, 47 give sums 115, 103, 89, 84, only 115 works, so B = 78. If F = 37 then A = 47, and (B + 47) must be a multiple of 5 — remaining ages 78, 66, 52, 24 give 125, 113, 99, 71, so B = 78. Both branches keep B = 78.
"The total of A and G is a prime number" and "G is divisible by 6." Among the ages, the multiples of 6 are 78 and 66; 78 is already taken by B, so G = 66. Check the prime clue: in the F = 37 branch, A = 47 and A + G = 47 + 66 = 113, which is prime. (The F = 24 branch is already dead: there F = 24 forces C = 37 from the C-F pair, while “just older than” makes A = 37 too, so A and C would share an age — impossible.) The consistent assignment is A = 47, F = 37, C = 24, D = 61, B = 78, G = 66, and E takes the last age, 52.
Therefore the age of G is 66 years.
Cross-check
Verify all clues with A = 47, B = 78, C = 24, D = 61, E = 52, F = 37, G = 66:
C + F = 24 + 37 = 61 = D ✔
G = 66 is divisible by 6 (66 = 6 × 11) ✔
A + G = 47 + 66 = 113, a prime number ✔
A = 47 is just older than F = 37 (no available age lies between 37 and 47) ✔
B + A = 78 + 47 = 125, divisible by 5 ✔
Every condition is satisfied, and the assignment is unique, so G = 66 years.