UPSC Prelims 2023·CSAT·Quantitative Aptitude·Arithmetic

For five children with ages a < b < c < d < e ; any two successive ages differ by 2 years. Question: What is the age of the youngest child? Statement- 1: The age of the eldest is 3 times the youngest. Statement- 2: The average age of the children is 8 years. Which one of the following is correct in respect of the above Question and the Statements?

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  1. AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
  2. BThe Question can be answered by using either Statement alone.Correct
  3. CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
  4. DThe Question cannot be answered even by using both the Statements together.

Explanation

The ages of the five children are a, a+2, a+4, a+6, a+8, where 'a' is the age of the youngest child. Statement 1: The age of the eldest is 3 times the youngest. The eldest age is a+8. The youngest age is a. So, a+8 = 3a. Subtract 'a' from both sides: 8 = 2a. Divide by 2: a = 4. Thus, Statement 1 alone is sufficient to find the age of the youngest child. Statement 2: The average age of the children is 8 years. The sum of the ages is a + (a+2) + (a+4) + (a+6) + (a+8) = 5a + 20. The average age is (5a + 20) / 5. Given that the average age is 8: (5a + 20) / 5 = 8. Multiply by 5: 5a + 20 = 40. Subtract 20: 5a = 20. Divide by 5: a = 4. Thus, Statement 2 alone is also sufficient to find the age of the youngest child. Since the question can be answered using either Statement alone, option B is correct.
Quantitative Aptitude: For five children with ages a < b < c < d < e ; any two successive ages differ by 2 years. Question: What is the age of
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