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 is the salary of $R$, in a group of $P$, $Q$, $R$, $S$ and $T$ whose average salary is ₹ 45980? I. Total of the salary of $P$ and $T$ is ₹ 90670. II. Total of the salary of $Q$ and $S$ is ₹ 76540.
Aptitude
Average
Difficulty: Easy
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 & Logic
To find the value of a specific item ($R$) within a larger set, you can subtract the sum of all other items from the total sum of the entire set.
$$Item = (Total \ Sum) - (Sum \ of \ Remaining \ Items)$$
### Step-by-Step Solution
**Given from the prompt:**
* The average salary of 5 people ($P, Q, R, S, T$) is ₹ 45980.
* Total salary of all 5 = $45980 \times 5 = 229900$.
* $$P + Q + R + S + T = 229900$$
**Evaluating Statement I:**
* $P + T = 90670$.
* This leaves $Q, R$, and $S$ unknown.
* Statement I alone is not sufficient.
**Evaluating Statement II:**
* $Q + S = 76540$.
* This leaves $P, R$, and $T$ unknown.
* Statement II alone is not sufficient.
**Evaluating Statements I and II Together:**
* Substitute both known sums into the total equation:
$$(P + T) + (Q + S) + R = 229900$$
$$90670 + 76540 + R = 229900$$
$$167210 + R = 229900$$
$$R = 229900 - 167210 = 62690$$
* By combining both statements, we can uniquely determine $R$'s salary.
### Exam Strategy & Shortcut
You don't need to compute $45980 \times 5$ or do the final subtraction during the exam! Just verify the variables. The prompt gives the sum for $P,Q,R,S,T$. Statement I knocks out $P$ and $T$. Statement II knocks out $Q$ and $S$. The only variable left standing is $R$. Since all other variables are accounted for, the data is sufficient.
### Common Pitfall
Wasting time doing the heavy arithmetic. Data sufficiency tests your logical reasoning regarding whether a problem *can* be solved, not your ability to act as a human calculator. The moment you see that substituting the chunks isolates $R$, mark "both necessary" and move on.
### Final Answer
**Therefore, the correct answer is If the data in both Statements I and II together are necessary to answer the question.**