995 practice questions covering Logical Reasoning, organised into 16 topics.
995 questions include a written explanation; 299 are from previous year papers.
Pick a topic below, or try the samples first.
Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?
A27
B36
C44
D45
Show answer and explanation
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.
Q2
Previous year questionmedium
Two Statements are given followed by two Conclusions:
Statements: All cats are dogs.
All cats are black.
Conclusion-I: All dogs are black.
Conclusion-II: Some dogs are not black.
Which of the above Conclusions logically follows/follow from the two given Statements, disregarding commonly known facts?
AOnly Conclusion-I
BOnly Conclusion-II
CNeither Conclusion-I nor Conclusion-II
DBoth Conclusion-I and Conclusion-II
Show answer and explanation
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.
Q3
Previous year questionmedium
Consider the following statements followed by two conclusions:
Statements: Some men are great. Some men are wise.
Conclusion I: Men are either great or wise.
Conclusion II: Some men are neither great nor wise.
Which one of the following is correct?
AOnly conclusion I is valid.
BOnly conclusion II is valid.
CBoth the conclusions are valid.
DNeither of the conclusion is valid.
Show answer and explanation
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.
Q4
Previous year questionmedium
Directions: Rotated positions of a single solid (a cube) are shown below. The various faces of the solid are marked with different symbols: a single dot, two dots, three dots, four dots, a cross and a line. By studying the rotated views, answer the item that follows.
What is the symbol on the face opposite to that containing two dots?
ASingle dot
BThree dots
CFour dots
DLine
Show answer and explanation
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.
Q5
Previous year questionmedium
Consider the following:
A + B means A is the son of B.
A - B means A is the wife of B.
What does the expression P + R - Q mean?
AQ is the son of P.
BQ is the wife of P.
CQ is the father of P.
DNone of the above
Show answer and explanation
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).
Q6
Previous year questionmedium
Consider the figure (a flower-like figure made of eight petal regions arranged around a central region) and answer the item that follows: What is the minimum number of different colours required to paint the figure given above such that no two adjacent regions have the same colour?
A3
B4
C5
D6
Show answer and explanation
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.
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