For five children with ages a < b < c < d < e, any two successive ages differ by 2 years. Question: What is…
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?
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
The Question can be answered by using either Statement alone.
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
The Question cannot be answered even by using both the Statements together.
Solution
The ages are $a, a+2, a+4, a+6, a+8$. Statement 1: eldest $= 3 \times$ youngest, so $a + 8 = 3a$, giving $a = 4$ — sufficient. Statement 2: average $= a + 4 = 8$, so $a = 4$ — sufficient. The question can be answered by either statement alone.