UPSC (Prelims) 2023 Logical Reasoning MCQ Questions

Consider the following:
I. A + B means A is neither smaller nor equal to B.
II. A – B means A is not greater than B.
III. A × B means A is not smaller than B.
IV. A ÷ B means A is neither greater nor equal to B.
V. A ≡ B means A is neither smaller nor greater than B.
Statement: P ÷ Q, P – T, T ÷ R, R ≡ S
Conclusion-1: Q ÷ T
Conclusion-2: S + Q
Which one of the following is correct in respect of the above Statement and the Conclusions?

40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child-7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again?

If 7 ⊕ 9 ⊕ 10 = 8, 9 ⊕ 11 ⊕ 17 = 5, 11 ⊕ 17 ⊕ 21 = 13, what is the value of 23 ⊕ 4 ⊕ 15?

For five children with ages a < b < c < d < e; any two consecutive ages differ by 2 years.
Question: What is the age of the youngest child?
Statement-1: The age of the oldest is 3 times the youngest.
Statement-2: The average age of the children is 8 years.
Which one of the following is correct in respect of the above Question and the Statements?

Question: Is p greater than q?
Statement-1: p × q is greater than zero.
Statement-2: p² is greater than q².
Which one of the following is correct in respect of the above Question and the Statements?

Consider the following including the Question and the Statements:
There are 5 members A, B, C, D, E in a family.
Question: What is the relation of E to B?
Statement-1: A and B are a married couple.
Statement-2: D is the father of C.
Statement-3: E is D's son.
Statement-4: A and C are sisters.
Which one of the following is correct in respect of the above Question and Statements?

Consider the sequence ABC__ABC_DABBCD_ABCD that follows a certain pattern. Which one of the following completes the sequence?

Three of the following five positive integers p, q, r, s, t are even and two of them are odd (not necessarily in order). Consider the following:

1. p + q + r − s − t is definitely even.
2. 2p + q + 2r − 2s + t is definitely odd.
   Which of the above statements is/are correct?

What is the middle term of the sequence Z, Z, Y, Y, X, X, X, W, W, W, W, ..., A?

A box contains 14 black balls, 20 blue balls, 26 green balls, 28 yellow balls, 38 red balls and 54 white balls. Consider the following statements:

1. The smallest number n such that any n balls drawn from the box randomly must contain at least one full group of at least one colour is 175.
2. The smallest number m such that any m balls drawn from the box randomly must contain at least one ball of each colour is 167.
   Which of the above statements is/are correct?

Consider a 3-digit number.
Question: What is the number?
Statement-1: The sum of the digits of the number is equal to the product of the digits.
Statement-2: The number is divisible by the sum of the digits of the number.
Which one of the following is correct in respect of the above Question and the Statements?

Question: Is (p + q + r) greater than (p – q + r), where p, q and r are integers?
Statement-1: (p – q) is positive.
Statement-2: (p – r) is negative.
Which one of the following is correct in respect of the above Question and the Statements?

Consider the following statements:

1. A is older than B.
2. C and D are of the same age.
3. E is the youngest.
4. F is younger than D.
5. F is older than A.
   How many statements given above are required to determine the oldest person/persons?

There are large number of silver coins weighing 2 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:

1. To buy 78 gm using these coins one must buy at least 7 coins.
2. To weigh 78 gm using these coins one can use less than 7 coins.
   Which of the statements given above is/are correct?

125 identical cubes are arranged in the form of a cubical block. How many cubes are surrounded by other cubes from each side?

Choose the group which is different from the others:

There are four letters and four envelopes and exactly one letter is to be put in exactly one envelope with the correct address. If the letters are randomly inserted into the envelopes, then consider the following statements:

1. It is possible that exactly one letter goes into an incorrect envelope.
2. There are only six ways in which only two letters can go into the correct envelopes.
   Which of the statements given above is/are correct?

Consider the following in respect of prime number p and composite number c:

1. p + c / (p − c) can be even.
2. 2p + c can be odd.
3. pc can be odd.
   Which of the statements given above are correct?

If 'ZERO' is written as 'CHUK', then how is 'PLAYER' written?

In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking tea also takes milk. Each person takes at least one drink.
Question: How many persons attended the party?
Statement-1: 50 persons took milk.
Statement-2: Number of persons who attended the party is five times the number of persons who took milk only.
Which one of the following is correct in respect of the above Question and the Statements?