Eight people: A, B, C, D, E, F, G and H.

Years: 1966, 1969, 1977, 1983, 1988, 1993, 2003 and 2008.

Steps:

1) The age of G is a perfect cube.

So, G was born in 1993.

2) The age of D is three times the age of C.

Here, D = 3 × C

51=3 × 17

So, D was born in 1969 and C was born in 2003.

3) The sum of the age of the A and the age of B is a prime number.

So, A+B=54+43=97

Here, two possible cases i.e. case 1 and case 2.

4) The HCF of the age of the H and F is 4.

The prime factorization of 32=2⁵ and the prime factorization of 12=2²×3¹

So, the HCF of 32 and 12=2²= 4.

Here, four possible cases i.e. case 1(a), case 1(b), case 2(a) and case 2(b).

5) The age difference between H and E is 5 years.

Here case 1(b) and case 2(b) get eliminated.

6) B was born just before E.

Here case 2(a) gets eliminated.

Final arrangement:

Here, B was born in 1977 and the age of B is 43.

So, the age of H is 32 years.

Hence, H is 11 years younger than B.

Eight people: A, B, C, D, E, F, G and H.

Years: 1966, 1969, 1977, 1983, 1988, 1993, 2003 and 2008.

Steps:

1) The age of G is a perfect cube.

So, G was born in 1993.

2) The age of D is three times the age of C.

Here, D = 3 × C

51=3 × 17

So, D was born in 1969 and C was born in 2003.

3) The sum of the age of the A and the age of B is a prime number.

So, A+B=54+43=97

Here, two possible cases i.e. case 1 and case 2.

4) The HCF of the age of the H and F is 4.

The prime factorization of 32=2⁵ and the prime factorization of 12=2²×3¹

So, the HCF of 32 and 12=2²= 4.

Here, four possible cases i.e. case 1(a), case 1(b), case 2(a) and case 2(b).

5) The age difference between H and E is 5 years.

Here case 1(b) and case 2(b) get eliminated.

6) B was born just before E.

Here case 2(a) gets eliminated.

Final arrangement:

Hence, the one who was born in 1969 was born immediately after A.

Eight people: A, B, C, D, E, F, G and H.

Years: 1966, 1969, 1977, 1983, 1988, 1993, 2003 and 2008.

Steps:

1) The age of G is a perfect cube.

So, G was born in 1993.

2) The age of D is three times the age of C.

Here, D = 3 × C

51=3 × 17

So, D was born in 1969 and C was born in 2003.

3) The sum of the age of the A and the age of B is a prime number.

So, A+B=54+43=97

Here, two possible cases i.e. case 1 and case 2.

4) The HCF of the age of the H and F is 4.

The prime factorization of 32=2⁵ and the prime factorization of 12=2²×3¹

So, the HCF of 32 and 12=2²= 4.

Here, four possible cases i.e. case 1(a), case 1(b), case 2(a) and case 2(b).

5) The age difference between H and E is 5 years.

Here case 1(b) and case 2(b) get eliminated.

6) B was born just before E.

Here case 2(a) gets eliminated.

Final arrangement:

Here, the age of E is 37 years, the age of F is 12 years and the age of C is 17 years.

So, (37+12+17) ÷3=66÷3=22

Hence, 22 years is the average of the age of E, the age of F and the age of C.

Eight people: A, B, C, D, E, F, G and H.

Years: 1966, 1969, 1977, 1983, 1988, 1993, 2003 and 2008.

Steps:

1) The age of G is a perfect cube.

So, G was born in 1993.

2) The age of D is three times the age of C.

Here, D = 3 × C

51=3 × 17

So, D was born in 1969 and C was born in 2003.

3) The sum of the age of the A and the age of B is a prime number.

So, A+B=54+43=97

Here, two possible cases i.e. case 1 and case 2.

4) The HCF of the age of the H and F is 4.

The prime factorization of 32=2⁵ and the prime factorization of 12=2²×3¹

So, the HCF of 32 and 12=2²= 4.

Here, four possible cases i.e. case 1(a), case 1(b), case 2(a) and case 2(b).

5) The age difference between H and E is 5 years.

Here case 1(b) and case 2(b) get eliminated.

6) B was born just before E.

Here case 2(a) gets eliminated.

Final arrangement:

Hence, F was born in 2003 is a false statement.

Eight people: A, B, C, D, E, F, G and H.

Years: 1966, 1969, 1977, 1983, 1988, 1993, 2003 and 2008.

Steps:

1) The age of G is a perfect cube.

So, G was born in 1993.

2) The age of D is three times the age of C.

Here, D = 3 × C

51=3 × 17

So, D was born in 1969 and C was born in 2003.

3) The sum of the age of the A and the age of B is a prime number.

So, A+B=54+43=97

Here, two possible cases i.e. case 1 and case 2.

4) The HCF of the age of the H and F is 4.

The prime factorization of 32=2⁵ and the prime factorization of 12=2²×3¹

So, the HCF of 32 and 12=2²= 4.

Here, four possible cases i.e. case 1(a), case 1(b), case 2(a) and case 2(b).

5) The age difference between H and E is 5 years.

Here case 1(b) and case 2(b) get eliminated.

6) B was born just before E.

Here case 2(a) gets eliminated.

Final arrangement:

Hence, ‘E-37’ is true combination.