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.
How many persons were born between A and B?
- A.
Two
- B.
More than four
- C.
Four
- D.
One
- E.
Three
Attempted by 5 students.
Show answer & explanation
Correct answer: E
Concept
In an age-based arrangement, first convert every birth year to an age using Age = Base year − Birth year, then translate each verbal clue (sum, divisibility, prime, "just older") into an arithmetic condition. Apply the most restrictive conditions first to fix unique people, then place the rest.
Application
The seven birth years give these ages (Base year 2025):
1947 → 78, 1959 → 66, 1964 → 61, 1973 → 52
1978 → 47, 1988 → 37, 2001 → 24
Now apply the clues in order:
G's age is divisible by 6. Among the ages, only 78 and 66 are multiples of 6, so G is 66 or 78.
Sum of ages of C and F equals the age of D. Searching the set, 24 + 37 = 61 is the only triple where two ages add to a third age, so {C, F} = {24, 37} and D = 61.
A is just older than F, meaning A's age is the value immediately above F's with no one in between. F must be 24 or 37 (from {C, F} = {24, 37}). If F = 24, then C = 37, and A — the next age above 24 — would also be 37, clashing with C; so this case is impossible. Hence F = 37, making A the next age up, 47, and C = 24.
Total age of A and G is a prime number. A = 47, so A + G must be prime. If G = 66, 47 + 66 = 113 (prime); if G = 78, 47 + 78 = 125 (not prime). Therefore G = 66.
Sum of B and A is divisible by 5. A = 47, and the remaining ages for B are 78 and 52. 47 + 78 = 125 is divisible by 5, while 47 + 52 = 99 is not, so B = 78 (and E = 52).
Final order from oldest to youngest: B (78), G (66), D (61), E (52), A (47), F (37), C (24).
Cross-check
C + F = 24 + 37 = 61 = D ✓; G = 66 is divisible by 6 ✓; A + G = 47 + 66 = 113 is prime ✓; A = 47 sits immediately above F = 37 ✓; B + A = 78 + 47 = 125 is divisible by 5 ✓. The persons standing between A and B in this line are G, D and E — that is 3 persons.