English and Logical Reasoning Prep Guide
- Exam
- English and Logical Reasoning Prep Guide
- Subject
- Logical Reasoning
- Chapter
- Data Sufficiency
English and Logical Reasoning Prep Guide · Logical Reasoning · Data Sufficiency
Directions: Each of the following consists of a question and two...
Directions: Each of the following consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question.
7 books namely Book 1, Book 2, Book 3, Book 4, Book 5, Book 6 and Book 7 are of different weights. Find the second lightest book?
Statement I :& Book 1 is heavier than Book 4, which is just lighter than Book 3. Book 2 is not the lightest. Book 5 is just heavier than Book 3.
Statement II :& Book 3 is heavier than only two books. Book 7 is just heavier than Book 1, which is heavier than Book 4. Book 4 is lighter than Book 3.
Statement I :& Book 1 is heavier than Book 4, which is just lighter than Book 3. Book 2 is not the lightest. Book 5 is just heavier than Book 3.
Statement II :& Book 3 is heavier than only two books. Book 7 is just heavier than Book 1, which is heavier than Book 4. Book 4 is lighter than Book 3.
Options
- AIf the data in statement I is sufficient to answer the question.
- BIf the data in statement II is sufficient to answer the question.
- CIf the data in either statement I or statement II is sufficient to answer the question.
- DIf the data in both statement I and statement II is necessary to answer the question.
Correct answer
D.
If the data in both statement I and statement II is necessary to answer the question.
Step-by-step solution
7 books namely Book 1, Book 2, Book 3, Book 4, Book 5, Book 6 and Book 7 are of different weights.
Find the second lightest book?
Statement I:& Book 1 is heavier than Book 4, which is just lighter than Book 3. Book 2 is not the lightest. Book 5 is just heavier than Book 3.
Statement II:& & Book 3 is heavier than only two books. Book 7 is just heavier than Book 1, which is heavier than Book 4. Book 4 is lighter than Book 3.
Checking statement I:
Following arrangement can be prepared with the given hints:
Book 1 > Book 5 > Book 3 > Book 4
But we cannot find the second lightest book because we don’t have information for all the books.
Hence data in statement I alone is not sufficient to answer the question.
Checking statement II:
Following arrangement can be prepared with the given hints:
Book 3> Book 4 > __ or& Book 3 > __ > Book 4
Thus Book 4 could be or could not be the second lightest book.
Hence data in statement II alone is not sufficient to answer the question.
Checking statements I and II:
Statement I:& Book 1 is heavier than Book 4, which is just lighter than Book 3. Book 2 is not the lightest. Book 5 is just heavier than Book 3.
Statement II:& Book 3 is heavier than only two books. Book 7 is just heavier than Book 1, which is heavier than Book 4. Book 4 is lighter than Book 3.
Using the hints given in italics, we can have the following arrangement.
Book 1> Book 3 > Book 4 > __
Thus we can determine Book 4 to be the second lightest book.
Hence data in both the statements is necessary to answer the question.
Hence option D is correct.
Find the second lightest book?
Statement I:& Book 1 is heavier than Book 4, which is just lighter than Book 3. Book 2 is not the lightest. Book 5 is just heavier than Book 3.
Statement II:& & Book 3 is heavier than only two books. Book 7 is just heavier than Book 1, which is heavier than Book 4. Book 4 is lighter than Book 3.
Checking statement I:
Following arrangement can be prepared with the given hints:
Book 1 > Book 5 > Book 3 > Book 4
But we cannot find the second lightest book because we don’t have information for all the books.
Hence data in statement I alone is not sufficient to answer the question.
Checking statement II:
Following arrangement can be prepared with the given hints:
Book 3> Book 4 > __ or& Book 3 > __ > Book 4
Thus Book 4 could be or could not be the second lightest book.
Hence data in statement II alone is not sufficient to answer the question.
Checking statements I and II:
Statement I:& Book 1 is heavier than Book 4, which is just lighter than Book 3. Book 2 is not the lightest. Book 5 is just heavier than Book 3.
Statement II:& Book 3 is heavier than only two books. Book 7 is just heavier than Book 1, which is heavier than Book 4. Book 4 is lighter than Book 3.
Using the hints given in italics, we can have the following arrangement.
Book 1> Book 3 > Book 4 > __
Thus we can determine Book 4 to be the second lightest book.
Hence data in both the statements is necessary to answer the question.
Hence option D is correct.