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. Who among the following was born in 2010?

The correct option is None of the above (as E was born in 2010).

Step-by-step Explanation:

Step 1: Calculate the ages of all 9 people as of December 31, 2021.

By subtracting each given birth year from 2021, we get the following ages:

• 2021 - 1998 = 23 years old

• 2021 - 2000 = 21 years old

• 2021 - 2003 = 18 years old

• 2021 - 2004 = 17 years old

• 2021 - 2005 = 16 years old

• 2021 - 2010 = 11 years old

• 2021 - 2012 = 9 years old

• 2021 - 2015 = 6 years old

• 2021 - 2017 = 4 years old

The complete set of ages is {23, 21, 18, 17, 16, 11, 9, 6, 4}.

Step 2: Find the ages of F, G, and I.

We are given that the ages of F, G, and I are all perfect squares, where I is the youngest and F is the oldest of the three.

The perfect squares in our age set are 16 (4²), 9 (3²), and 4 (2²).

• F (oldest) = 16 years old (Born in 2005)

• G (middle) = 9 years old (Born in 2012)

• I (youngest) = 4 years old (Born in 2017)

Remaining ages: {23, 21, 18, 17, 11, 6}

Step 3: Find 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.

From the remaining ages, the pair that sums to 35 is 18 and 17 (18 + 17 = 35).

• C = 18 years old (Born in 2003)

• D = 17 years old (Born in 2004)

Remaining ages: {23, 21, 11, 6}

Step 4: Find the ages of A and B.

We are given that B is two years younger than A.

From the remaining ages, the two ages with a difference of 2 years are 23 and 21 (23 - 21 = 2).

• A = 23 years old (Born in 1998)

• B = 21 years old (Born in 2000)

Remaining ages: {11, 6}

Step 5: Find the ages of E and H.

We are given that E is older than H.

From the remaining ages {11, 6}:

• E = 11 years old (Born in 2010)

• H = 6 years old (Born in 2015)

Final Arrangement:

• 1998 (23 years) – A

• 2000 (21 years) – B

• 2003 (18 years) – C

• 2004 (17 years) – D

• 2005 (16 years) – F

• 2010 (11 years) – E

• 2012 (9 years) – G

• 2015 (6 years) – H

• 2017 (4 years) – I

Therefore, E was born in 2010. Since E is not among options A, D, B, or C, the correct option is None of the above.