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 age of A?

The correct option is 53 years.

Step-by-Step Explanation:

Step 1: Calculate the age of each person based on the year 2022.

Given birth years: 1969, 1973, 1978, 1982, 1988, 1990, 1995.

Calculating ages with respect to the base year 2022:

• 2022 - 1969 = 53 years old

• 2022 - 1973 = 49 years old

• 2022 - 1978 = 44 years old

• 2022 - 1982 = 40 years old

• 2022 - 1988 = 34 years old

• 2022 - 1990 = 32 years old

• 2022 - 1995 = 27 years old

Let's arrange the birth years and their corresponding ages in descending order of age (from oldest to youngest):

1. 1969 — 53 years

2. 1973 — 49 years

3. 1978 — 44 years

4. 1982 — 40 years

5. 1988 — 34 years

6. 1990 — 32 years

7. 1995 — 27 years

Step 2: Place C and E using their age condition.

Condition: "C is two years elder than E."

Looking at the calculated ages, the only pair of ages with a difference of 2 years (where C is elder than E) is 34 and 32.

• Age of C = 34 years (born in 1988)

• Age of E = 32 years (born in 1990)

Step 3: Determine D's position.

Condition: "The number of persons born after E is same as the number of persons born before D."

• E was born in 1990, which is the 6^th position in chronological order (only 1 person, born in 1995, was born after E).

• Therefore, exactly 1 person was born before D, which means D must be the 2^nd oldest person.

• D was born in 1973 (Age of D = 49 years).

Step 4: Determine F's age.

Condition: "The age difference between F and E is a perfect cube number."

Age of E = 32 years.

Let's test possible perfect cubes for the age difference |Age(F) - 32|:

• If difference is 1³ = 1: Age of F could be 33 or 31 (Not in our list of ages).

• If difference is 2³ = 8: Age of F could be 32 - 8 = 24 (Not in list) or 32 + 8 = 40 (Present in list!).

• If difference is 3³ = 27: Age of F could be 32 + 27 = 59 or 32 - 27 = 5 (Not in list).

Thus, Age of F must be 40 years (born in 1982).

Step 5: Determine B's age.

Condition: "The difference between the age of D and B is a prime number."

Age of D = 49 years.

Available remaining ages for B, A, and G are 53, 44, and 27.

Let's check the age difference |49 - Age(B)| for each remaining age:

• If Age(B) = 53: |49 - 53| = 4 (Not a prime number)

• If Age(B) = 44: |49 - 44| = 5 (5 is a prime number! Valid.)

• If Age(B) = 27: |49 - 27| = 22 (Not a prime number)

Therefore, B's age must be 44 years (born in 1978).

Step 6: Place A and G.

Condition: "A is older than G."

The two remaining unassigned ages are 53 years (1969) and 27 years (1995).

Since A is older than G:

• Age of A = 53 years (born in 1969)

• Age of G = 27 years (born in 1995)

Final Arrangement Summary:

• A: Born in 1969 (53 years old)

• D: Born in 1973 (49 years old)

• B: Born in 1978 (44 years old)

• F: Born in 1982 (40 years old)

• C: Born in 1988 (34 years old)

• E: Born in 1990 (32 years old)

• G: Born in 1995 (27 years old)

Hence, the age of A is 53 years.