Logical Reasoning MCQs for UPSC Prelims

Correct answer: D - 45

Option (d) is correct. A wearable pair means a left shoe and a right shoe of the same colour. The box has 54 shoes: 20 red (10 left, 10 right), 18 white and 16 black. In the worst case Raj first draws all 18 white and all 16 black shoes (34 attempts), and then 10 red shoes that are all for the same foot, say all 10 left ones (44 attempts), still without a wearable red pair. The 45th attempt must produce a right red shoe and complete the pair, so the maximum number of attempts is 45. Option (a) 27 is just one shoe from each pair and guarantees nothing. Option (b) 36 would be the answer only if any two red shoes counted as a pair (34 non-red plus 2 red); some coaching keys initially reported 36 on that reading, but a pair of shoes to wear requires a left and a right, and the official UPSC answer key confirms 45. Option (c) 44 is the worst case that still lacks a pair; one more attempt is needed to guarantee it.

Correct answer: C - Neither Conclusion-I nor Conclusion-II

From 'all cats are dogs' and 'all cats are black', we only know that the cats (a subset of dogs) are black. The colour of dogs that are not cats is undetermined. Conclusion-I (all dogs are black) need not hold, because non-cat dogs might be any colour. Conclusion-II (some dogs are not black) also need not hold, because it is possible that every dog happens to be black. Since each conclusion is only a possibility and not a certainty, neither follows.

Correct answer: D - Neither of the conclusion is valid.

The premises are particular: 'some men are great' and 'some men are wise'. Conclusion I claims all men are either great or wise, which is a universal claim not supported by two 'some' statements, so it is invalid. Conclusion II claims some men are neither great nor wise, but the premises do not guarantee the existence of such men (the great and the wise could together cover all the men referred to), so it is only a possibility, not a certainty, and is therefore invalid. Since neither follows necessarily, the answer is that neither conclusion is valid.

Correct answer: C - Four dots

A cube has three pairs of opposite faces. Tracking the symbols that appear together (adjacent) across the rotated views lets us eliminate every face that shares an edge with the two-dot face, since adjacent faces can never be opposite. Across the views, the two-dot face is seen alongside the single dot, three dots, the cross and the line, so none of these can lie opposite it. The only symbol never adjacent to the two-dot face is the four-dot face, which must therefore be its opposite. Hence the answer is Four dots.

Correct answer: C - Q is the father of P.

Read the expression left to right using the defined operators. 'P + R' means P is the son of R, so R is a parent of P. 'R - Q' means R is the wife of Q. So R is the wife of Q and R is P's mother (a parent), which makes Q the husband of R and therefore the father of P. Hence (c) Q is the father of P. The official UPSC answer key marks this (c).

Correct answer: A - 3

The figure has eight outer petal regions arranged in a ring around one central region. Going around the ring, alternate petals do not touch each other, so the petals can be coloured with just two colours used alternately (colour 1, colour 2, colour 1, colour 2, ...); since there is an even number of petals this alternation is consistent. The central region touches every petal, so it must take a third colour distinct from both. Therefore the minimum number of colours needed is 3.