UPSC Prelims 1997 · General Studies
Question 146: Logical Reasoning and Mental Ability
Examine the following statements regarding a set of balls: I. All balls are black. II. All balls are white. III. Only some balls are black. IV. No balls are black. Assuming that the balls can only be black or white, which two statements given above can both be true, but cannot both be false? Choose the correct answer from the codes given below:
AnswerThe answer is (a).
I (all balls black) and IV (no ball black) are the all-against-none pair. They cannot both hold for any actual set of balls, and both fail when the balls are a mixture, which is when III holds. The key picks this opposed pair.
Why each option is right or wrong
- (a) The all-against-none pair the key picks: they cannot both be true, and both are false for a mixture of balls.
- (b) I and III cannot both hold; both are false if all balls are white.
- (c) II and III cannot both hold; both are false if all balls are black.
- (d) III and IV cannot both hold; both are false if all balls are black.
Worth knowing: As printed, the question asks for a pair that cannot both be false, which no pair here is; the key fits the reverse wording (cannot both be true, can both be false), which all four options satisfy.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 1997, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.