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?

20233Mprelimsupscyear-2023p2logical-reasoningdata-sufficiency
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.
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.Correct
Explanation & Solution

The correct answer is (D) The Question cannot be answered even by using both the Statements together..

Explanation:

We are given five children with ages a < b < c < d < e, where any two successive ages differ by 2 years. Thus, let the ages be: a, a+2, a+4, a+6, a+8. We need to find the age of the youngest child (a). Statement-1: The age of the eldest is 3 times the youngest => e = 3a => a + 8 = 3a => 2a = 8 => a = 4. Thus Statement-1 alone gives the unique age of the youngest child as 4. Statement-2: The average age of the children is 8 years. The sum of ages = 5 × 8 = 40. Sum = a + (a+2) + (a+4) + (a+6) + (a+8) = 5a + 20 = 40 => 5a = 20 => a = 4. Thus Statement-2 alone also gives the unique age of the youngest child as 4. Therefore, the question can be answered by using either Statement alone. Option (b) is correct.

हिंदी में प्रश्न एवं आदर्श उत्तर

पांच बच्चों के लिए, जिनकी आयु a < b < c < d < e क्रम में है; किसी भी दो उत्तरोत्तर आयु के बीच 2 वर्ष का अंतर है ।
प्रश्न : सबसे छोटे बच्चे की आयु क्या है ?
कथन-1 : सबसे बड़े बच्चे की आयु सबसे छोटे बच्चे की आयु की तीन गुनी है ।
कथन-2 : बच्चों की औसत आयु 8 वर्ष है ।

उपर्युक्त प्रश्न और कथनों के बारे में निम्नलिखित में से कौन-सा एक सही है ?

A.इस प्रश्न का उत्तर, दोनों में से किसी एक कथन का अकेले उपयोग कर दिया जा सकता है, किंतु दूसरे कथन का अकेले उपयोग कर नहीं दिया जा सकता ।
B.इस प्रश्न का उत्तर, दोनों में से किसी भी एक कथन का अकेले उपयोग कर दिया जा सकता है ।
C.इस प्रश्न का उत्तर, दोनों कथनों का एक साथ उपयोग कर दिया जा सकता है, किंतु दोनों में से किसी एक कथन का अकेले उपयोग कर नहीं दिया जा सकता ।
D.इस प्रश्न का उत्तर, दोनों कथनों का एक साथ उपयोग करके भी नहीं दिया जा सकता ।सही

सही उत्तर (D) The Question cannot be answered even by using both the Statements together. है।

व्याख्या:

We are given five children with ages a < b < c < d < e, where any two successive ages differ by 2 years. Thus, let the ages be: a, a+2, a+4, a+6, a+8. We need to find the age of the youngest child (a). Statement-1: The age of the eldest is 3 times the youngest => e = 3a => a + 8 = 3a => 2a = 8 => a = 4. Thus Statement-1 alone gives the unique age of the youngest child as 4. Statement-2: The average age of the children is 8 years. The sum of ages = 5 × 8 = 40. Sum = a + (a+2) + (a+4) + (a+6) + (a+8) = 5a + 20 = 40 => 5a = 20 => a = 4. Thus Statement-2 alone also gives the unique age of the youngest child as 4. Therefore, the question can be answered by using either Statement alone. Option (b) is correct.

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