Analyze the given details thoroughly and solve the query that follows.

Seven individuals were born in different years: 1985, 1992, 1994, 1998, 1999, 2001 and 2004. Their respective ages are determined using 2022 as the base year. The age gap between G and K is 7 years. F is 3 years older than K. The count of individuals born between F and G equals the count of individuals born between S and D. The number of individuals born after S is equal to the number of individuals born before L. H is not the eldest among them.

The number of individuals born between G and K is half the number of individuals born between ____ and ____.

Correct Answer: S, K

Step-by-Step Explanation:

Step 1: Calculate the age and birth year of each individual using 2022 as the base year.

Let's list the given birth years in chronological order and calculate the age of individuals born in these years with respect to the base year 2022:

• Born in 1985 → Age = 2022 - 1985 = 37 years

• Born in 1992 → Age = 2022 - 1992 = 30 years

• Born in 1994 → Age = 2022 - 1994 = 28 years

• Born in 1998 → Age = 2022 - 1998 = 24 years

• Born in 1999 → Age = 2022 - 1999 = 23 years

• Born in 2001 → Age = 2022 - 2001 = 21 years

• Born in 2004 → Age = 2022 - 2004 = 18 years

Step 2: Determine the positions based on clues.

1. "The age gap between G and K is 7 years."
Looking at the ages: (37, 30), (28, 21).
So, the possible pairs for (G, K) in terms of birth years are (1985, 1992) or (1994, 2001).

2. "F is 3 years older than K."
Since F is 3 years older than K, the age of F = Age of K + 3 (which means F was born 3 years before K).
• If K is born in 1992 (age 30), then F's age is 33, but no one is 33 years old.
• If K is born in 2001 (age 21), then F's age is 24 (born in 1998). This is valid!
Therefore, K is born in 2001 and F is born in 1998.

3. Since K is born in 2001, from the pair (G, K) with a 7-year age gap, G must be born in 1994 (age 28).

4. "The count of individuals born between F and G equals the count of individuals born between S and D."
Birth years: 1985, 1992, 1994 (G), 1998 (F), 1999, 2001 (K), 2004.
Between G (1994) and F (1998), there are 0 individuals (since no one was born in 1995-1997 in our given list).
Therefore, the number of individuals born between S and D must also be 0. This means S and D are born in consecutive years in the given list.

5. "The number of individuals born after S is equal to the number of individuals born before L."
Let's analyze the remaining available birth years: 1985, 1992, 1999, 2004 for S, D, L, H.
Since H is not the eldest (born in 1985), 1985 must be occupied by someone else.
If L is born in 1985 (0 people before L), then S must be born in 2004 (0 people after S).
Since S and D are consecutive, D must be born in 1999.
This leaves H to be born in 1992.

Step 3: Final arrangement by birth year:

• 1985: L

• 1992: H

• 1994: G

• 1998: F

• 1999: D

• 2001: K

• 2004: S

Step 4: Answer the question.

The number of individuals born between G (1994) and K (2001) is 2 (namely, F and D).

We need to find two individuals between whom the number of individuals born is double this amount (i.e., 2 × 2 = 4 individuals).

Let's check the number of individuals born between S (2004) and K (2001): there is 0.

Wait, between S (2004) and K (2001), there are 0 individuals. But let's check between S (2004) and K (2001) in the options:
• Between S (2004) and K (2001): 0 individuals.
• Between F (1998) and S (2004): 2 individuals (D, K).
• Between L (1985) and H (1992): 0 individuals.
• Between S (2004) and D (1999): 1 individual (K).
• Between S (2004) and K (2001)? Let's re-verify S, K: S is 2004, K is 2001 → 0 individuals.
Wait, if G and K have 2 individuals between them, then 2 is half of 4. Between S (2004) and K (2001) or S and K in the list: S (2004) and K (2001) has 0. Let's check between S (2004) and H (1992) = 4 individuals (G, F, D, K), or S (2004) and K (2001) if S is 1985 and L is 2004!

If S is born in 1985 and L is born in 2004:
• 0 people before S, 0 people after L.
• Since S (1985) and D are consecutive, D is born in 1992.
• Remaining position for H is 1999 (not 1985, which satisfies "H is not the eldest").
Let's check this arrangement:
• 1985: S
• 1992: D
• 1994: G
• 1998: F
• 1999: H
• 2001: K
• 2004: L

Now let's count between G (1994) and K (2001): F and H are born between them, so there are 2 individuals.

Number of individuals born between S (1985) and K (2001):
The people born between S and K are D (1992), G (1994), F (1998), and H (1999) — total 4 individuals!

Since 2 is half of 4, the number of individuals born between G and K is half the number of individuals born between S and K.