Each of the questions given below consists of a statement and / or a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statement(s) is / are sufficient to answer the given question. Read both the statements and give answer. What marks have been obtained by Arun? I. Arun's marks are the average of marks of Nitin and Manick. II. Nitin obtained 80 marks and this is 25% more than the marks obtained by Manick.
Aptitude
Average
Difficulty: Medium
Choose an option
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AIf the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question
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BIf the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
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CIf the data either in Statement I or in Statement II alone are sufficient to answer the question
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DIf the data even in both Statements I and II together are not sufficient to answer the question
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EIf the data in both Statements I and II together are necessary to answer the question
Answer
Correct Answer: If the data in both Statements I and II together are necessary to answer the question
Explanation
### Concept & Strategy
To find a specific individual's value (Arun's marks), we need to trace the dependency chain. If Arun depends on Nitin and Manick, we must be able to determine the exact values for both Nitin and Manick.
### Step-by-Step Solution
**Evaluating Statement I:**
* We are given that Arun's marks are the average of Nitin's and Manick's marks.
$$Arun = \frac{Nitin + Manick}{2}$$
* We do not have the values for Nitin or Manick.
* Statement I alone is not sufficient.
**Evaluating Statement II:**
* We are given Nitin's marks = 80.
* Nitin's marks are 25% more than Manick's marks.
$$80 = Manick \times (1 + \frac{25}{100})$$
$$80 = 1.25 \times Manick$$
$$Manick = \frac{80}{1.25} = 64$$
* We now know Nitin (80) and Manick (64), but this statement tells us nothing about Arun.
* Statement II alone is not sufficient.
**Evaluating Statements I and II Together:**
* From Statement II, we have Nitin = 80 and Manick = 64.
* From Statement I, we know $Arun = \frac{Nitin + Manick}{2}$.
* Substituting the values:
$$Arun = \frac{80 + 64}{2} = \frac{144}{2} = 72$$
* By combining both statements, we get a unique value for Arun.
### Exam Strategy & Shortcut
Read the dependencies backwards. The question asks for Arun. Statement I links Arun to Nitin and Manick (Requires N & M). Statement II provides Nitin and a link to find Manick (Provides N & M). Therefore, combining them will inevitably yield Arun. You do not need to calculate the actual values (80 and 64) during the exam.
### Common Pitfall
A major trap is calculating Manick's marks incorrectly by subtracting 25% of 80 (getting 60 instead of 64). 25% more than Manick means $1.25 \times Manick = 80$, not $Manick = 80 - (0.25 \times 80)$. However, because this is Data Sufficiency, even if you make this calculation error, you will still correctly deduce that both statements are needed.
### Final Answer
**Therefore, the correct answer is If the data in both Statements I and II together are necessary to answer the question.**