Read the given information carefully and answer the following questions.

Six persons A to F were born on the same date in October in six different years, namely 1980, 1985, 1988, 1992, 1995, and 1998. Their ages are calculated as of 2026. Each person likes a different color among Red, Blue, Green, Yellow, Orange, and Purple. All the above information is not necessarily in the same order.

A is the oldest person. The one who likes Green is younger than the one who likes Red, and the difference between their ages is 8. Two persons were born between the one who likes Blue and E. D was born immediately before E, who likes Orange. The sum of the digits of the year in which F was born is 27.

In which of the subsequent pairs is the difference in age greater than 8 years?

Correct Answer: A, E

Let's solve the logical puzzle step-by-step to find the birth year, age, and color preference for each person (A to F).

Step 1: Calculate the age of each person as of the year 2026.
The given birth years are 1980, 1985, 1988, 1992, 1995, and 1998.
Calculating ages as of 2026:
• Born in 1980: Age = 2026 - 1980 = 46 years
• Born in 1985: Age = 2026 - 1985 = 41 years
• Born in 1988: Age = 2026 - 1988 = 38 years
• Born in 1992: Age = 2026 - 1992 = 34 years
• Born in 1995: Age = 2026 - 1995 = 31 years
• Born in 1998: Age = 2026 - 1998 = 28 years

Step 2: Determine F's birth year using the sum of digits clue.
Clue: "The sum of the digits of the year in which F was born is 27."
Let's check the sum of digits for each birth year:
• 1980: 1 + 9 + 8 + 0 = 18
• 1985: 1 + 9 + 8 + 5 = 23
• 1988: 1 + 9 + 8 + 8 = 26
• 1992: 1 + 9 + 9 + 2 = 21
• 1995: 1 + 9 + 9 + 5 = 24
• 1998: 1 + 9 + 9 + 8 = 27
Thus, F was born in 1998 (Age = 28).

Step 3: Determine A's birth year and placing D, E, and Blue.
Clue: "A is the oldest person."
The oldest person was born in the earliest year, so A was born in 1980 (Age = 46).

Clue: "D was born immediately before E, who likes Orange."
This means D and E were born in two consecutive birth years in the list. The available consecutive year pairs are:
• Pair 1: 1985 and 1988
• Pair 2: 1992 and 1995

Clue: "Two persons were born between the one who likes Blue and E."
• If E was born in 1988 (Pair 1), two persons between Blue and E means Blue would be in 1998 (F likes Blue).
• If E was born in 1995 (Pair 2), two persons between Blue and E means Blue would be in 1985.

Clue: "The one who likes Green is younger than the one who likes Red, and the difference between their ages is 8."
Looking at the age differences between people:
• 46 - 38 = 8 (Birth years 1980 and 1988)
• 36 - 28 = 8 (Wait, our ages are 46, 41, 38, 34, 31, 28)
Let's check the differences between all available ages:
• 46 - 38 = 8 (1980 and 1988)
• 34 - 26 (Not in list)
So the only two ages with a difference of 8 are 46 (born 1980) and 38 (born 1988).
Since the one who likes Green is younger than the one who likes Red:
• Red = born 1980 (A likes Red)
• Green = born 1988 (Age 38 likes Green)

Since the person born in 1988 likes Green, E (who likes Orange) cannot be born in 1988.
Therefore, E must be born in 1995 (Age = 31), and D (born immediately before E) must be born in 1992 (Age = 34).
Since E is born in 1995, two persons were born between Blue and E, which means the person born in 1985 likes Blue.
The remaining person B must be born in 1985 (Age = 41).

Step 4: Summary of persons, birth years, and ages.
• 1980: A, Age = 46, Color = Red
• 1985: B, Age = 41, Color = Blue
• 1988: C, Age = 38, Color = Green
• 1992: D, Age = 34
• 1995: E, Age = 31, Color = Orange
• 1998: F, Age = 28

Step 5: Check the age difference for the given options.
We need to find the pair with an age difference greater than 8 years:
• Option D, F: Age difference = 34 - 28 = 6 years (Not > 8)
• Option D, E: Age difference = 34 - 31 = 3 years (Not > 8)
• Option A, E: Age difference = 46 - 31 = 15 years (15 > 8)
• Option E, F: Age difference = 31 - 28 = 3 years (Not > 8)
• Option A, B: Age difference = 46 - 41 = 5 years (Not > 8)

Thus, the pair (A, E) has an age difference of 15 years, which is greater than 8 years.