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.

What is the difference between the age of A and G?

Correct Answer: The correct option is 26 years.

Let us solve the puzzle step-by-step to determine the birth year and age of each person based on the base year 2022.

Step 1: Calculate the age of each person for their respective birth years (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

The calculated ages are: 53, 49, 44, 40, 34, 32, 27.

Step 2: Use the clues to determine the positions of E, C, F, D, B, A, and G
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.
Therefore, C's age = 34 years (born in 1988) and E's age = 32 years (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 6th birth year in chronological order (only 1995 is after 1990).
So, 1 person was born after E.
This means 1 person must be born before D. Thus, D is the 2nd person in chronological order, born in 1973 (Age = 49 years).

3. "The age difference between F and E is a perfect cube number."
E's age is 32. Perfect cubes are 1, 8, 27, 64, etc.
Let us check possible age differences with 32:
• |53 - 32| = 21 (Not a cube)
• |49 - 32| = 17 (Not a cube)
• |44 - 32| = 12 (Not a cube)
• |40 - 32| = 8 (Which is 2³, a perfect cube!)
• |27 - 32| = 5 (Not a cube)
Therefore, F's age must be 40 years (born in 1982).

4. "The difference between the age of D and B is a prime number."
D's age is 49 years. The remaining unassigned ages are 53, 44, and 27.
Let's check the differences between 49 and the remaining ages:
• |49 - 53| = 4 (Not prime)
• |49 - 44| = 5 (Prime number!)
• |49 - 27| = 22 (Not prime)
Therefore, B's age must be 44 years (born in 1978).

5. "A is older than G."
The two remaining unassigned ages are 53 and 27.
Since A is older than G, A's age = 53 years (born in 1969) and G's age = 27 years (born in 1995).

Summary of Person, Birth Year, and Age:
• A: Born in 1969, Age = 53
• D: Born in 1973, Age = 49
• B: Born in 1978, Age = 44
• F: Born in 1982, Age = 40
• C: Born in 1988, Age = 34
• E: Born in 1990, Age = 32
• G: Born in 1995, Age = 27

Step 3: Calculate the difference between the age of A and G

$\text{Difference}=\text{Age of A}-\text{Age of G}$

$\text{Difference}=53-27=26\text{years}$

Hence, the difference between the age of A and G is 26 years.