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. John had an average score of 85 in three tests. What was John's lowest score? I. John's highest score was 95. II. Average of John's two highest scores was 92.
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 Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question
Explanation
### Concept & Logic
If you know the total sum of a set of items, and you are given the exact sum of a specific subset of those items, you can find the value of the remaining item by simple subtraction.
$$Total \ Sum = (Sum \ of \ Two \ Highest) + Lowest \ Score$$
### Step-by-Step Solution
**Given:**
* Average of 3 tests = 85.
* Total sum of all 3 tests = $85 \times 3 = 255$.
**Evaluating Statement I:**
* The highest score is 95.
* Sum of the remaining two tests = $255 - 95 = 160$.
* These two tests could be 80 and 80, or 70 and 90. We cannot uniquely identify the lowest score.
* Statement I alone is not sufficient.
**Evaluating Statement II:**
* The average of the two highest scores is 92.
* Sum of the two highest scores = $92 \times 2 = 184$.
* Since there are only 3 tests in total, the remaining test MUST be the lowest score.
* Lowest score = Total Sum - Sum of Two Highest
* Lowest score = $255 - 184 = 71$.
* We have a unique, definitive answer.
* Statement II alone is sufficient.
### Exam Strategy & Shortcut
Think of the group as blocks. The prompt gives you the total weight of 3 blocks. Statement II gives you the exact combined weight of the two heaviest blocks. Subtracting the heaviest blocks from the total leaves exactly one block remaining, which by definition must be the lightest (lowest). No complex calculation is needed during the exam—just verify the logic and mark Statement II as sufficient.
### Common Pitfall
Students often hesitate on Statement II, wondering "what if the two highest scores are identical?" (e.g., 92 and 92). It doesn't matter. Whether they are 92 and 92, or 94 and 90, their sum is strictly locked at 184. The remaining test is always unequivocally $255 - 184 = 71$.
### Final Answer
**Therefore, the correct answer is If 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.**