If Pen < Pencil, Pencil < Book and Book > Cap, then which one of the following is always true?
- (a) Pen > Cap
- (b) Pen < Book ✓ UPSC's answer
- (c) Pencil = Cap
- (d) Pencil > Cap
Why the answer is (b)
• The given inequalities are Pen < Pencil, Pencil < Book, and Book > Cap.
• Combining the first two statements (Pen < Pencil and Pencil < Book) establishes a transitive relationship: Pen < Book.
• The third statement (Book > Cap) indicates that Book is greater than Cap, but it does not establish a direct relationship between Pen and Cap, nor between Pencil and Cap.
• Since Pen is less than Pencil and Pencil is less than Book, Pen must necessarily be less than Book.
• Therefore, the statement 'Pen < Book' is always true based on the transitive property of inequality.
Why the other options are wrong
- (a) Pen > Cap
- The relationship between Pen and Cap cannot be determined because there is no direct or transitive link connecting them through the given inequalities.
- (c) Pencil = Cap
- There is no information provided that equates Pencil and Cap; in fact, their relationship is indeterminate.
- (d) Pencil > Cap
- The relationship between Pencil and Cap cannot be determined because the inequality Book > Cap does not specify how Pencil compares to Cap.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.