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.

What is the total number of individuals who are older than H?

Options

A

5

B

3

C

1

D

2

E

None of these

Show Answer

Correct Answer :

Option E

None of these

Solution :

Correct Answer: None of these


Let's solve this step-by-step by determining the exact birth year and age of each of the seven individuals based on the base year 2022.


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

The given birth years arranged in ascending order (from oldest to youngest) are:

1. Birth year 1985: Age = 2022 - 1985 = 37 years

2. Birth year 1992: Age = 2022 - 1992 = 30 years

3. Birth year 1994: Age = 2022 - 1994 = 28 years

4. Birth year 1998: Age = 2022 - 1998 = 24 years

5. Birth year 1999: Age = 2022 - 1999 = 23 years

6. Birth year 2001: Age = 2022 - 2001 = 21 years

7. Birth year 2004: Age = 2022 - 2004 = 18 years


Step 2: Analyze the clues to place the individuals.

1. "F is 3 years older than K."

Looking at the ages (37, 30, 28, 24, 23, 21, 18), the only pairs of ages with a difference of 3 years are:

- 24 and 21 (1998 and 2001)

Therefore, F must be born in 1998 (age 24) and K must be born in 2001 (age 21).


2. "The age gap between G and K is 7 years."

Since K's age is 21 years (born in 2001), G's age can be either:

- 21+7=28 years (born in 1994), OR

- 21-7=14 years (not an available age).

Hence, G must be born in 1994 (age 28).


3. "The count of individuals born between F and G equals the count of individuals born between S and D."

The birth years in order are: 1985, 1992, 1994 (G), 1998 (F), 1999, 2001 (K), 2004.

Between G (1994) and F (1998), exactly 1 person was born (in 1992 is before G, 1994 G, 1998 F -> wait, order of years: 1985, 1992, 1994 (G), 1998 (F), 1999, 2001 (K), 2004).

Between 1994 and 1998, there is 0 people born in our list of given birth years (the years are 1994 and 1998 with no given year in between). So, 0 individuals were born between F and G.

Thus, 0 individuals must be born between S and D, which means S and D were born in consecutive available birth years.


4. "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 bottom (youngest), L is at position x from the top (oldest).

The remaining open positions for birth years are: 1985, 1992, 1999, 2004.

- Position 1 (1985)

- Position 2 (1992)

- Position 5 (1999)

- Position 7 (2004)

Since S and D are consecutive in the list, S and D can be (1985, 1992).

If S is born in 1985 (Position 1, oldest): 0 people born before S. Then L must be born in 2004 (Position 7, youngest), so 0 people born after L (number born after S = 6, number born before L = 6).

Let's verify: If S = 1985 (6 born after S), L = 2004 (6 born before L). Then D = 1992.

Now the remaining unassigned birth year is 1999, which must belong to H.


5. "H is not the eldest among them."

H is born in 1999, which is not the eldest (1985 is the eldest). This condition is satisfied!


Final Arrangement of Birth Years (from Oldest to Youngest):

1. 1985: S (Age 37)

2. 1992: D (Age 30)

3. 1994: G (Age 28)

4. 1998: F (Age 24)

5. 1999: H (Age 23)

6. 2001: K (Age 21)

7. 2004: L (Age 18)


Question: What is the total number of individuals who are older than H?

H was born in 1999 (age 23).

The individuals older than H are those born before 1999:

S (1985), D (1992), G (1994), and F (1998).

There are exactly 4 individuals older than H.


Since 4 is not present in options ["5", "3", "1", "2"], the correct choice is None of these.

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