Data sufficiency - determining age of youngest child
Question
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?
Options
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.
Explanation
The ages form an Arithmetic Progression (AP) with a common difference of 2[cite: 4061, 4062]. Let the ages be represented as: a, a+2, a+4, a+6, a+8.
Statement 1: The eldest (e = a+8) is 3 times the youngest (a)[cite: 4061, 4064]: a + 8 = 3a \implies 2a = 8 \implies a = 4 years. This yields a unique solution. Sufficient .
Statement 2: The average age is 8 years. For an odd number of terms in an AP, the average matches the middle term exactly. Middle term c = a + 4 = 8 \implies a = 4 years. This also yields a unique solution independently. Sufficient.
Answer: (b).
Question details
Year
2023
Paper
CSAT
Question
Q60
Section
Data Interpretation & Sufficiency
Sub-topic
Data Sufficiency
Type
Data sufficiency
Difficulty
Medium
Source hint
Data sufficiency
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