Directions: Each question consists of two conclusions followed by some…
2024
Directions: Each question consists of two conclusions followed by some statements. Consider the given conclusions to be true even if they seem to be at variance with commonly known facts. Read the conclusions and then decide which of the following statement is true for given conclusions.
Conclusions:
I. All number can never be digit
II. Some digit being letter is a possibility
- A.
Statements: All series is number; Some series is digit; Only a few letter is number
- B.
Statements: Only a few series is digit; All series is number; Some letter is number
- C.
Statements: No digit is series; No series is number; All number is letter
- D.
Statements: Only digit is letter; Some digit is number; Only a few series is number
- E.
Statements: No digit is letter; Only a few letter is number; Only a few number is series
Attempted by 1 students.
Show answer & explanation
Correct answer: B
Concept
In a statement-conclusion (reverse syllogism) problem the two conclusions are fixed, and you must pick the single statement set from which BOTH conclusions definitely follow. Three rules govern this: a definite negative (“No X is Y”) makes that overlap permanently impossible; any set that leaves a denied overlap open fails the conclusion that denies it; and a “possibility” conclusion holds only when no statement definitely blocks that overlap. Read “All number can never be digit” as “it must be guaranteed that at least one number is NOT a digit” (so “all numbers are digits” is ruled out), and “Some digit being letter is a possibility” as “the digit–letter overlap must stay possible.” Note “Only a few X is Y” means some X are Y and some X are NOT Y.
Applying it to each set
{All series is number; Some series is digit; Only a few letter is number}: this forces some number to be a digit but never forces any number to lie outside digit, so “all numbers are digits” is left open — conclusion I is not secured.
{Only a few series is digit; All series is number; Some letter is number}: “only a few series is digit” gives series that are NOT digit, and since every series is a number, those are numbers that are not digits — so “all numbers are digits” is impossible, securing conclusion I; with no statement forbidding a digit from being a letter, the digit–letter overlap of conclusion II stays open. Both follow.
{No digit is series; No series is number; All number is letter}: nothing here pushes any number outside digit, so “all numbers are digits” is not ruled out — conclusion I is not secured.
{Only digit is letter; Some digit is number; Only a few series is number}: this guarantees some number IS a digit but never that some number is NOT a digit, leaving “all numbers are digits” open — conclusion I is missed.
{No digit is letter; Only a few letter is number; Only a few number is series}: “No digit is letter” permanently blocks any digit from being a letter, so the overlap demanded by conclusion II can never happen.
Cross-check
Only the set {Only a few series is digit; All series is number; Some letter is number} satisfies both conclusions at once: it guarantees a number outside digit (conclusion I) while leaving the digit–letter overlap free (conclusion II). Each rejected set breaks exactly one of the two conclusions, confirming this is the unique consistent choice.