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 ?
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
- (b) The Question can be answered by using either Statement alone. ✓ UPSC's answer
- (c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
- (d) The Question cannot be answered even by using both the Statements together.
Why the answer is (b)
• Let the ages of the five children be a, a+2, a+4, a+6, and a+8, where 'a' is the age of the youngest child.
• Using Statement-1: The eldest child's age is a+8. The statement says a+8 = 3a, which simplifies to 2a = 8, giving a = 4. This uniquely determines the youngest child's age.
• Using Statement-2: The average age is 8. The sum of ages is 5 * 8 = 40. The sum of the arithmetic progression is 5a + (2+4+6+8) = 5a + 20.
• Setting 5a + 20 = 40 gives 5a = 20, so a = 4. This also uniquely determines the youngest child's age.
• Since both statements independently yield the same unique value for 'a', the question can be answered by either statement alone.
Why the other options are wrong
- (a) The Question can be answered by using one of the Statements alone, but cannot be answered…
- This option is incorrect because both statements individually provide sufficient information to determine the age of the youngest child.
- (c) The Question can be answered by using both the Statements together, but cannot be…
- This option is incorrect because the statements do not need to be used together; each one is sufficient on its own.
- (d) The Question cannot be answered even by using both the Statements together.
- This option is incorrect because the age of the youngest child can be definitively calculated as 4 years using either statement.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2023, held on 28 May 2023. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.