Question Details

Study the given information carefully and answer the questions given below.

Nine people A, B, C, D, E, F, G, H, and I were born in different years i.e., 1998, 2000, 2003, 2004, 2005, 2010, 2012, 2015, and 2017 on the same date i.e., 31st December but not necessarily in the same order. Their ages are calculated as of 31st December 2021.

B is two years younger than A. The sum of the ages of C and D is 35, and C is older than D. The ages of F, G, and I are all perfect squares, where I is the youngest of the three and F is the oldest of the three. E is older than H.

Which of the following individuals is the oldest?

Options

A

C

B

B

C

Either B or C

D

Either A or B

E

A

Show Answer

Correct Answer :

Option E

A

Solution :

To find the oldest individual, let's step-by-step calculate the age of each person as of 31st December 2021 based on their given birth years.

Step 1: Calculate the age of each person for each birth year.
The given birth years are 1998, 2000, 2003, 2004, 2005, 2010, 2012, 2015, and 2017.
Age in 2021 = 2021 - Birth Year:
• Born in 1998: 2021 - 1998 = 23 years old
• Born in 2000: 2021 - 2000 = 21 years old
• Born in 2003: 2021 - 2003 = 18 years old
• Born in 2004: 2021 - 2004 = 17 years old
• Born in 2005: 2021 - 2005 = 16 years old
• Born in 2010: 2021 - 2010 = 11 years old
• Born in 2012: 2021 - 2012 = 9 years old
• Born in 2015: 2021 - 2015 = 6 years old
• Born in 2017: 2021 - 2017 = 4 years old

The available ages are: 23, 21, 18, 17, 16, 11, 9, 6, 4.

Step 2: Identify the ages of F, G, and I using the perfect square condition.
The ages of F, G, and I are all perfect squares.
Looking at our calculated list of ages (23, 21, 18, 17, 16, 11, 9, 6, 4), the perfect square ages are 16 (42), 9 (32), and 4 (22).
We are given that I is the youngest of the three and F is the oldest of the three.
Therefore:
• F's age = 16 years old (born in 2005)
• G's age = 9 years old (born in 2012)
• I's age = 4 years old (born in 2017)

Step 3: Determine the ages of C and D.
We are given that the sum of the ages of C and D is 35, and C is older than D.
Remaining available ages (excluding 16, 9, 4): 23, 21, 18, 17, 11, 6.
Let's check which two ages from this list sum to 35:
• 18 + 17 = 35
Since C is older than D:
• C's age = 18 years old (born in 2003)
• D's age = 17 years old (born in 2004)

Step 4: Determine the ages of A and B.
We are given that B is two years younger than A.
Remaining available ages (excluding 16, 9, 4, 18, 17): 23, 21, 11, 6.
Looking for two ages with a difference of 2 years:
• 23 - 21 = 2
Since B is 2 years younger than A:
• A's age = 23 years old (born in 1998)
• B's age = 21 years old (born in 2000)

Step 5: Determine the ages of E and H.
The remaining ages are 11 and 6.
We are given that E is older than H:
• E's age = 11 years old (born in 2010)
• H's age = 6 years old (born in 2015)

Conclusion:
The ages of all nine individuals are:
• A = 23 (Oldest)
• B = 21
• C = 18
• D = 17
• F = 16
• E = 11
• G = 9
• H = 6
• I = 4 (Youngest)

Thus, A is the oldest individual.

The correct option is A.

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