Question Details

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.

Find the difference between the ages of L and F.

Options

A

None of these

B

12 years

C

8 years

D

9 years

E

6 years

Show Answer

Correct Answer :

Option E

6 years

Solution :

The correct option is 6 years.


Step 1: Calculate the age of each individual based on the base year 2022.

The given birth years are 1985, 1992, 1994, 1998, 1999, 2001, and 2004.

Calculating the ages with respect to 2022:

- Born in 1985: 2022 - 1985 = 37 years
- Born in 1992: 2022 - 1992 = 30 years
- Born in 1994: 2022 - 1994 = 28 years
- Born in 1998: 2022 - 1998 = 24 years
- Born in 1999: 2022 - 1999 = 23 years
- Born in 2001: 2022 - 2001 = 21 years
- Born in 2004: 2022 - 2004 = 18 years


Step 2: Determine the positions of G, K, and F.

The age gap between G and K is 7 years. Looking at the ages (37, 30, 28, 24, 23, 21, 18), the pairs with a difference of 7 years are:

- (30, 23), which corresponds to years (1992, 1999)
- (28, 21), which corresponds to years (1994, 2001)

We are given that F is 3 years older than K. Thus, the age of K must allow someone (F) to be 3 years older (i.e., Age of F = Age of K + 3).

Let's test the possible values for K:

If K = 21 years (born in 2001):
Then F = 21 + 3 = 24 years (born in 1998). This is valid since 24 is one of the ages.
Since K = 21, then G = 28 (born in 1994) to satisfy the 7-year age gap.

Let's check the other possibility for K:
If K = 30 years (born in 1992), F would be 33, which is not in the list.
If K = 23 years (born in 1999), F would be 26, which is not in the list.
If K = 28 years (born in 1994), F would be 31, which is not in the list.

Therefore, the positions for F, G, and K are uniquely determined:

- G is born in 1994 (Age = 28)
- F is born in 1998 (Age = 24)
- K is born in 2001 (Age = 21)


Step 3: Determine the positions of the remaining individuals.

The count of individuals born between F (1998) and G (1994) is 1 (the person born in 1992 is before 1994, between 1994 and 1998 is only 1992? No, ordered years: 1985, 1992, 1994, 1998, 1999, 2001, 2004).

List of years in chronological order:

1st: 1985
2nd: 1992
3rd: 1994 (G)
4th: 1998 (F)
5th: 1999
6th: 2001 (K)
7th: 2004

The number of individuals born between G (3rd) and F (4th) is 0.

Since the count of individuals born between F and G equals the count of individuals born between S and D, there must be 0 individuals born between S and D. This means S and D are born in consecutive years.

We are also given: "The number of individuals born after S is equal to the number of individuals born before L."

This symmetry means if S is at position x from the top/bottom, L is at position x from the opposite side.

The available positions for S, D, L, H are 1985 (1st), 1992 (2nd), 1999 (5th), and 2004 (7th).

The only consecutive pair among available years is (1985, 1992), which are positions 1st and 2nd.

So S and D occupy positions 1st and 2nd (1985 and 1992).

If S is 2nd (1992), 1 person is before S. Then L must have 1 person after him, so L would be 6th (2001), but 2001 is already K. Thus, S cannot be 2nd.

If S is 1st (1985), 0 people are before S? The clue says "number of individuals born after S is equal to the number of individuals born before L."
If S is at 1st position (1985), 6 people are born after S, so 6 people must be born before L, placing L at the 7th position (2004).

Since S is 1st (1985), D must be 2nd (1992).

The remaining empty position is 5th (1999), which must be occupied by H (Age = 23).

We check the condition "H is not the eldest among them": H is born in 1999 (age 23), which is true as S (born in 1985) is the eldest.


Complete Arrangement:

1985 (Age 37): S
1992 (Age 30): D
1994 (Age 28): G
1998 (Age 24): F
1999 (Age 23): H
2001 (Age 21): K
2004 (Age 18): L


Step 4: Find the difference between the ages of L and F.

Age of F = 24 years

Age of L = 18 years

Difference = 24 - 18 = 6 years

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