Given:

Persons: Q, U, R, L, M, O, T and X.

Years: 1956, 1959, 1964, 1978, 1985, 1987, 1995, 2011.

1) T’s age is a prime number.

2) Q’s age is a perfect square but not the eldest.

Here, we get 2 cases i.e. Case 1 and Case 2:

3) Only three persons were born between Q and X.

4) Only one person was born between X and O.

Here, we get one more case i.e. Case 1b.

5) M’s age is an even number, who was born after X.

Here, Case-2 will be eliminated.

6) U was born immediately before R.

Here, case 1-b will be eliminated. Hence, case 1-a will be our final arrangement.

Here, O is related to X in such a way that only one person was born in between O and X. In the same way, only one person was born in between T and M.

Clearly, only one person was born in between R and L.

Hence, L is the correct answer.

Given:

Persons: Q, U, R, L, M, O, T and X.

Years: 1956, 1959, 1964, 1978, 1985, 1987, 1995, 2011.

1) T’s age is a prime number.

2) Q’s age is a perfect square but not the eldest.

Here, we get 2 cases i.e. Case 1 and Case 2:

3) Only three persons were born between Q and X.

4) Only one person was born between X and O.

Here, we get one more case i.e. Case 1b.

5) M’s age is an even number, who was born after X.

Here, Case-2 will be eliminated.

6) U was born immediately before R.

Here, case 1-b will be eliminated. Hence, case 1-a will be our final arrangement.

Clearly, M does not belong to that group because except M, ages of other persons are in odd numbers.

Given:

Persons: Q, U, R, L, M, O, T and X.

Years: 1956, 1959, 1964, 1978, 1985, 1987, 1995, 2011.

1) T’s age is a prime number.

2) Q’s age is a perfect square but not the eldest.

Here, we get 2 cases i.e. Case 1 and Case 2:

3) Only three persons were born between Q and X.

4) Only one person was born between X and O.

Here, we get one more case i.e. Case 1b.

5) M’s age is an even number, who was born after X.

Here, Case-2 will be eliminated.

6) U was born immediately before R.

Here, case 1-b will be eliminated. Hence, case 1-a will be our final arrangement.

Clearly, R’s age is divisible by 11 who was born immediately before Q.

Hence, ‘The one who was born immediately before Q’ is the correct answer.

Given:

Persons: Q, U, R, L, M, O, T and X.

Years: 1956, 1959, 1964, 1978, 1985, 1987, 1995, 2011.

1) T’s age is a prime number.

2) Q’s age is a perfect square but not the eldest.

Here, we get 2 cases i.e. Case 1 and Case 2:

3) Only three persons were born between Q and X.

4) Only one person was born between X and O.

Here, we get one more case i.e. Case 1b.

5) M’s age is an even number, who was born after X.

Here, Case-2 will be eliminated.

6) U was born immediately before R.

Here, case 1-b will be eliminated. Hence, case 1-a will be our final arrangement.

Clearly, O is the eldest person.

Hence, O is the correct answer.

Given:

Persons: Q, U, R, L, M, O, T and X.

Years: 1956, 1959, 1964, 1978, 1985, 1987, 1995, 2011.

1) T’s age is a prime number.

2) Q’s age is a perfect square but not the eldest.

Here, we get 2 cases i.e. Case 1 and Case 2:

3) Only three persons were born between Q and X.

4) Only one person was born between X and O.

Here, we get one more case i.e. Case 1b.

5) M’s age is an even number, who was born after X.

Here, Case-2 will be eliminated.

6) U was born immediately before R.

Here, case 1-b will be eliminated. Hence, case 1-a will be our final arrangement.

Cleary, the age of X is 56 years.

Hence, ‘56 years’ is the correct answer.