Logical Deductions 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: 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.

Correct answer: B - 22

To minimise working days we maximise holidays, which requires the shortest month: February of a non-leap year (28 days = exactly 4 complete weeks). In 4 weeks there are exactly 4 Sundays and 4 Saturdays. Holidays = all 4 Sundays + the 2nd and 4th Saturdays = 4 + 2 = 6 holidays. Working days = 28 - 6 = 22. Longer months (30 or 31 days) give more working days, and a leap-year February (29 days) gives at least 22 as well, so the minimum is 22. Hence (b) 22. The official UPSC key marks this (b) 22.

Correct answer: D - Data are inadequate

We know Neha > Randhir, and Randhir > Kunal + Debu, so Randhir > Kunal and Randhir > Debu. Also Kunal + Shankar > Randhir, and Sonal > Shankar. So both Neha and Sonal are 'large', but there is no relation given that compares Neha with Sonal directly, nor any that ranks Sonal against Randhir/Neha numerically. Either Neha or Sonal could be the highest depending on values. Since the data do not fix a single highest scorer, the answer is (d) Data are inadequate.

Correct answer: C - Both Statement-1 and Statement-2 are required to answer the Question

From Statement-2 alone, C > A > D, but nothing is known about B and E relative to C, so it cannot crown the heaviest - insufficient. Statement-1 says A and D each outweigh B, E and F, and that none of them is the heaviest; since C is the only person Statement-1 never weighs against anyone, the statement by itself does not directly establish C's position, so on the official reading Statement-1 alone is also not sufficient. Combining the two: B, E (and F) are below A and D, and C > A > D places C above everyone, so C is the heaviest only when both statements are used together - option (c). Note on the dispute: the official UPSC key accepted both (c) and (d) for this item because the two options overlap (both assert that neither statement alone suffices), while some coaching keys argued for (a) by elimination (if neither A nor D is heaviest, only C remains). The official key is followed here with (c); confidence is marked low because of this conflict. Option (b) is clearly wrong since Statement-2 says nothing about B and E.

Correct answer: C - Fifth

If F is second, then F is not the highest, so by the rule 'either C or F scores the highest', C must be the highest. Whenever C is highest, E scores the least, so E is ranked sixth. The remaining ranks 3, 4 and 5 are filled by D, A and B. Using D > A > B (from D > A and A > B), the order is D third, A fourth, B fifth. Hence B is fifth, option (c).

Correct answer: A - 1 and 3

Two statements that cannot both be true but can both be false are contraries (the universal affirmative 'All A are B' and the universal negative 'No A is B'). Statement 1 (All animals are carnivorous) and statement 3 (No animals are carnivorous) cannot both be true; yet both are false if some animals are carnivorous and some are not. The other pairs are contradictories (1 and 2, or 3 and 4), which cannot both be false. Hence the answer is 1 and 3.

Correct answer: D - 6

P = 4. The difference between P and T is 5, so T = 4 + 5 = 9 (4 - 5 = -1 is not in the 1 to 9 range). The difference between N and T is 3, so N = 9 - 3 = 6 (9 + 3 = 12 is out of range). Hence N = 6.