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. If there is an average of 250 words on each page, how many pages can Michael read in an hour? I. There is an average of 25 ten-word lines on each page. II. Michael can read 30 ten-word lines per minute.
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 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 & Strategy
To determine the number of pages read per hour, we need to bridge the gap between words (or lines) and time.
$$Pages \ per \ Hour = \frac{Total \ Words \ Read \ in \ an \ Hour}{Words \ per \ Page}$$
The question already gives us the denominator (250 words per page). We just need to find a statement that gives us Michael's reading speed.
### Step-by-Step Solution
**Given:**
* Words per page = 250.
* Target: Pages read in 60 minutes.
**Evaluating Statement I:**
* It states there are 25 lines of 10 words each per page ($25 \times 10 = 250$ words).
* This merely confirms the information already given in the question prompt. It provides zero information about Michael's reading speed.
* Statement I alone is not sufficient.
**Evaluating Statement II:**
* Michael reads 30 lines per minute, where each line is 10 words.
* Reading speed = $30 \times 10 = 300$ words per minute.
* Words per hour = $300 \times 60 = 18000$ words per hour.
* Pages per hour = $\frac{18000}{250} = 72$ pages.
* We can successfully calculate a unique answer using only this statement.
* Statement II alone is sufficient.
### Exam Strategy & Shortcut
Data Sufficiency questions often contain "dummy" statements that just repeat or break down the premise. Statement I breaks 250 into $25 \times 10$. The moment you see a statement just rephrasing the given prompt without introducing the missing link (Michael's speed), eliminate it instantly. Statement II provides a clear speed metric, completing the puzzle.
### Common Pitfall
A common mistake is thinking both statements are needed because Statement I defines what a "ten-word line" is for Statement II. However, "ten-word line" is a self-explanatory phrase. Statement II contains all the necessary mathematical values ($30 \times 10$ words/min) on its own.
### 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.**