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Q60·CSAT · Prelims 2023

Data sufficiency - determining age of youngest child

DI / DSData SufficiencyData sufficiencyMedium

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

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.

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.

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.

For evenly spaced series (Arithmetic Progressions), the average is always identically equal to the exact middle term, allowing you to bypass long summation formulas.

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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