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UPSC Prelims 2023CSATBasic NumeracyData Sufficiency - Arithmetic Progression

Q70. For five children with ages a < b < c < d < e; any two successive ages differs 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

A. The Question can be answered by using one of the Statement alone.
B. The Question can be answered by using either Statement alone.✓ Correct
C. The Question can be answered by using both the Statement together, but cannot be answered using either Statement alone.
D. The Question cannot be answered even by using both the Statements together.

Detailed Solution

✓ Correct Answer: Option B

Let the age of the youngest child be 'a'. Since successive ages differ by 2 years, the ages of the five children are a, a+2, a+4, a+6, and a+8. Statement 1: The age of the eldest is 3 times the youngest.

So, a+8 = 3a. This simplifies to 2a = 8, which means a = 4. Since we found a unique value for 'a', Statement 1 alone is sufficient. Statement 2: The average age of the children is 8 years.

The sum of their ages is a + (a+2) + (a+4) + (a+6) + (a+8) = 5a + 20. The average is (5a + 20) / 5 = a + 4. Given that the average is 8, we have a + 4 = 8, which means a = 4. Since we found a unique value for 'a', Statement 2 alone is sufficient.

As either statement alone is sufficient to answer the question, option (B) is the correct choice.

All Basic Numeracy Questions →All Data Sufficiency - Arithmetic Progression Questions →← Back to Full Paper

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