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 sets is true for the given conclusions.

Conclusions:

I. All number can never be digit
II. Some digit being letter is a possibility

  1. A.

    Statements: All series is number; Some series is digit; Only a few letter is number

  2. B.

    Statements: Only a few series is digit; All series is number; Some letter is number

  3. C.

    Statements: No digit is series; No series is number; All number is letter

  4. D.

    Statements: Only digit is letter; Some digit is number; Only a few series is number

  5. E.

    Statements: No digit is letter; Only a few letter is number; Only a few number is series

Attempted by 7 students.

Show answer & explanation

Correct answer: C

Concept

In a reverse syllogism, you are given the conclusions and must pick the statement set from which they follow. A definite negative conclusion of the form "X can never be Y" means "No X is Y" must hold; a possibility conclusion ("Some A being B is a possibility") only needs to be NOT contradicted by the statements. So reject any set that FORCES the opposite of conclusion I, or that makes conclusion II impossible.

What the conclusions demand

  • Conclusion I "All number can never be digit" = No number is digit must hold, so the set must NOT force "Some number is digit".

  • Conclusion II "Some digit being letter is a possibility" = the set must leave "Some digit is letter" possible, so it must NOT force "No digit is letter".

Testing each statement set

  1. All series is number; Some series is digit; Only a few letter is number: "Some series is digit" with "All series is number" gives "Some number is digit" - this forces the opposite of conclusion I, so it is ruled out.

  2. Only a few series is digit; All series is number; Some letter is number: "Only a few series is digit" still asserts "Some series is digit", which with "All series is number" again yields "Some number is digit" - opposite of conclusion I, ruled out.

  3. No digit is series; No series is number; All number is letter: no statement links number with digit, so "Some number is digit" is NOT forced and "No number is digit" stays consistent (conclusion I holds); digit and letter are unconstrained, so "Some digit is letter" remains possible (conclusion II holds). Both conclusions survive.

  4. Only digit is letter; Some digit is number; Only a few series is number: "Some digit is number" directly gives "Some number is digit" - opposite of conclusion I, ruled out.

  5. No digit is letter; Only a few letter is number; Only a few number is series: "No digit is letter" makes "Some digit is letter" impossible - it kills conclusion II, ruled out.

Cross-check

Four of the five sets each contain a statement that directly contradicts one of the two conclusions; only the set "No digit is series; No series is number; All number is letter" leaves both conclusions intact, so it is the set from which the given conclusions follow.

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