Directions: Each of the questions given below consists of a question followed by three statements. You have to study the question and the statements and decide which of the statement(s) is/are necessary to answer the question. What is the average weight of girls in the class? I. Average weight of all the 60 students is 42 kg. II. Average weight of boys is 43 kg. III. Total weight of all girls together is 1144 kg.
Aptitude
Average
Difficulty: Medium
Choose an option
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AI and II only
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BII and III only
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CAll I, II and III
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DAny two of the three
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EQuestion cannot be answered even with information in all three statements
Answer
Correct Answer: All I, II and III
Explanation
## Concept & Logic
To find the average weight of a specific subgroup (girls), we need two exact values: the total weight of that subgroup and the total count of individuals in that subgroup.
$$ \text{Average}_{\text{girls}} = \frac{\text{Total Weight}_{\text{girls}}}{\text{Number of Girls}} $$
## Step-by-Step Solution
* **Goal Identification:** We need $\text{Total Weight}_{\text{girls}}$ and $\text{Number of Girls}$ ($G$).
* **Evaluate Statement III:** This directly provides the $\text{Total Weight}_{\text{girls}} = 1144$ kg. We still need $G$.
* **Evaluate Statement I:** Gives total students = $60$ and their average = $42$ kg.
Total weight of class = $60 \times 42 = 2520$ kg.
This alone doesn't give $G$.
* **Evaluate Combinations:**
From I and III, we can find the total weight of boys = $2520 - 1144 = 1376$ kg.
Now, to find the number of boys ($B$), we need their average weight.
Statement II provides the average weight of boys = $43$ kg.
With II, we can calculate $B = 1376 / 43 = 32$.
Finally, since total students = $60$, we can find $G = 60 - 32 = 28$.
Now we have both parts for our initial formula: $1144 / 28$.
## Exam Strategy & Shortcut
In Data Sufficiency, map out the dependencies backwards.
Target -> Total Girl Weight & Girl Count.
Total Girl Weight -> Found in III.
Girl Count -> Needs Total Count (I) & Boy Count.
Boy Count -> Needs Total Boy Weight & Boy Average (II).
Total Boy Weight -> Needs Total Class Weight (I) & Total Girl Weight (III).
Since every piece of the chain requires information from I, II, and III, all three are strictly necessary. Do not perform the actual divisions during the exam!
## Common Pitfall
Students often waste 30-40 seconds doing the heavy arithmetic ($1376 / 43$) to prove it works. In data sufficiency, if you establish a clear algebraic path to the answer with no missing links, stop and mark the option.
## Final Answer
**Therefore, the correct answer is All I, II and III.**