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 following years was D born?

The correct answer is 1992.

Step-by-step Explanation:

Step 1: Calculate the ages of each person as of 2026 based on their birth years.

The given birth years are 1980, 1985, 1988, 1992, 1995, and 1998.

Calculating each age as of 2026:

• 2026 - 1980 = 46 years old
• 2026 - 1985 = 41 years old
• 2026 - 1988 = 38 years old
• 2026 - 1992 = 34 years old
• 2026 - 1995 = 31 years old
• 2026 - 1998 = 28 years old

Step 2: Determine the birth year of F.

The clue states that the sum of the digits of the year in which F was born is 27.

Let us 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

Therefore, F was born in 1998.

Step 3: Determine the birth year of A.

The clue states that A is the oldest person. The oldest age is 46 (born in 1980).

Therefore, A was born in 1980.

Step 4: Find the positions of D and E.

We are given that:

1. E likes Orange.
2. D was born immediately before E.
3. Two persons were born between the one who likes Blue and E.

Let's look at the remaining birth years available: 1985, 1988, 1992, 1995.

Since D was born immediately before E, they must occupy consecutive birth years in the list [1980, 1985, 1988, 1992, 1995, 1998].

Possibility 1: D = 1985, E = 1988.
If E is born in 1988 (index 3), then 2 persons between Blue and E means Blue must be at index 6 (1998, which is F). This is valid.

Possibility 2: D = 1988, E = 1992.
If E is born in 1992 (index 4), 2 persons between Blue and E means Blue could be at index 1 (1980, which is A). This is valid.

Possibility 3: D = 1992, E = 1995.
If E is born in 1995 (index 5), 2 persons between Blue and E means Blue would be at index 2 (1985). This is valid.

Step 5: Apply the Green and Red age difference condition.

The clue states: "The one who likes Green is younger than the one who likes Red, and the difference between their ages is 8."

Looking at our calculated ages: [46, 41, 38, 34, 31, 28].

The only pair of ages with a difference of 8 years ($46-38=8$) is 46 and 38.

• The person aged 46 (born in 1980, which is A) likes Red.
• The person aged 38 (born in 1988) likes Green.

Since A (1980) likes Red, A cannot like Blue!

This eliminates Possibility 2 (where A/1980 liked Blue).

Also, 1988 likes Green, so E (who likes Orange) cannot be born in 1988. This eliminates Possibility 1 (where E was 1988).

Thus, Possibility 3 must be true:

• D was born in 1992.
• E was born in 1995 (likes Orange).
• The person born in 1985 likes Blue.

Final Arrangement Summary:

• 1980: A (Red, age 46)
• 1985: C or B (Blue, age 41)
• 1988: C or B (Green, age 38)
• 1992: D (Yellow/Purple, age 34)
• 1995: E (Orange, age 31)
• 1998: F (Yellow/Purple, age 28)

Therefore, D was born in the year 1992.