Directions (74-78): Study the following information carefully and answer the questions given below.

Seven persons- A, B, C, D, E, F and G were born in different years – 1969, 1973, 1978, 1982, 1988, 1990 and 1995 but not necessarily in the same order. Age of each person is calculated on the base year 2022. C is two years elder than E. The age difference between F and E is a perfect cube number. The number of persons born after E is same as the number of persons born before D. The difference between the age of D and B is a prime number. A is older than G.

Which among the following statement(s) is/are true?
I. A is the oldest among all
II. C was born in 1988
III. No one born after E

Correct Answer: Both I and II

Let's solve the puzzle step-by-step by determining the birth year and age of each person based on the base year 2022.

Step 1: Calculate the age of each person in the base year 2022
- 1969: 2022 - 1969 = 53 years old
- 1973: 2022 - 1973 = 49 years old
- 1978: 2022 - 1978 = 44 years old
- 1982: 2022 - 1982 = 40 years old
- 1988: 2022 - 1988 = 34 years old
- 1990: 2022 - 1990 = 32 years old
- 1995: 2022 - 1995 = 27 years old

Step 2: Determine the positions based on given clues
1. "C is two years elder than E."
Looking at the ages: (53, 49, 44, 40, 34, 32, 27), the only pair of ages with a difference of 2 years (where C is elder) is 34 and 32.
So, Age of C = 34 (born in 1988) and Age of E = 32 (born in 1990).

2. "The number of persons born after E is same as the number of persons born before D."
E is born in 1990, which is the 6^th person in order of birth year (only 1995 is after 1990).
So, exactly 1 person is born after E (1995).
Therefore, exactly 1 person must be born before D, which means D was born in the second oldest year, 1973 (Age of D = 49).

3. "The age difference between F and E is a perfect cube number."
Age of E = 32.
Possible perfect cubes are 1, 8, 27, etc.
Let's check the age difference between E (32) and other available ages (53, 44, 40, 27):
- |53 - 32| = 21 (Not a cube)
- |44 - 32| = 12 (Not a cube)
- |40 - 32| = 8 (Which is 2³, a perfect cube!)
- |27 - 32| = 5 (Not a cube)
Hence, F must be 40 years old (born in 1982).

4. "The difference between the age of D and B is a prime number."
Age of D = 49.
Remaining available ages for B, A, and G are: 53 (1969), 44 (1978), and 27 (1995).
Let's check differences with D's age (49):
- |49 - 53| = 4 (Not a prime)
- |49 - 44| = 5 (Prime number!)
- |49 - 27| = 22 (Not a prime)
So, Age of B = 44 (born in 1978).

5. "A is older than G."
The remaining ages are 53 (1969) and 27 (1995).
Since A is older than G:
- Age of A = 53 (born in 1969)
- Age of G = 27 (born in 1995)

Final Arrangement:
- 1969 (53 years): A
- 1973 (49 years): D
- 1978 (44 years): B
- 1982 (40 years): F
- 1988 (34 years): C
- 1990 (32 years): E
- 1995 (27 years): G

Step 3: Evaluate the statements
- Statement I: A is the oldest among all. -> True (A was born in 1969).
- Statement II: C was born in 1988. -> True (C's birth year is 1988).
- Statement III: No one born after E. -> False (G was born in 1995, after E).

Thus, statements I and II are true.