Logical Reasoning — Practice Questions
CSAT-pattern logical reasoning practice — syllogism, seating arrangement, blood relation, letter series, calendar and clock questions with fully worked solutions.
Questions
These are original CSAT-pattern practice questions written for this site — not past UPSC papers. Draw a diagram for each before choosing an option. Target time: about 9 minutes for all six.
Statements:
- Some cats are dogs.
- No dog is a rat.
Conclusions:
- I. Some cats are not rats.
- II. No cat is a rat.
Which of the conclusions logically follow(s)?
Solution
“Some A are B” + “No B is C” → “Some A are not C”. The cats that are dogs can never be rats, so I follows.
For II, draw a cat circle that overlaps dogs and rats (the rat circle stays clear of dogs). Both statements hold, but some cats are rats — so II does not follow.
Answer: A
Five friends A, B, C, D and E sit in a row facing north.
- B sits at one of the extreme ends.
- C sits to the immediate right of A.
- D sits exactly in the middle.
- E sits somewhere to the left of D.
Who sits at the extreme right end?
Solution
D is at position 3 (condition 3). A and C are adjacent with C on the right, so they occupy positions 1–2 or 4–5.
- Case 1: A = 1, C = 2. B must be at an end → B = 5. Then E = 4, which is to the right of D — violates condition 4.
- Case 2: A = 4, C = 5. B = 1. E = 2 (left of D) ✓.
| Position | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|
| Person | B | E | D | A | C |
C is at the extreme right.
Answer: C
Introducing a man, a woman said, “He is the only son of the mother of my father.” How is the man related to the woman?
Solution
“The mother of my father” = her paternal grandmother. The only son of the paternal grandmother is the woman’s father himself. (An uncle would need the grandmother to have a second son, which “only son” rules out.)
Answer: A
What comes next in the series: Z, X, U, Q, L, ?
Solution
Positions: Z = 26, X = 24, U = 21, Q = 17, L = 12. Gaps: −2, −3, −4, −5. Next gap −6: $12 - 6 = 6$ → F.
Answer: B
If 1 January 2025 was a Wednesday, what day of the week was 1 January 2026?
Solution
2025 is not divisible by 4, so it is an ordinary year: $365 = 52 \times 7 + 1$ → 1 odd day. Wednesday + 1 = Thursday.
Answer: D
How many times do the hour hand and the minute hand of a clock coincide in a day of 24 hours?
Solution
The minute hand gains $6^\circ - 0.5^\circ = 5.5^\circ$ per minute, i.e. $330^\circ$ per hour, on the hour hand. It gains a full $360^\circ$ every $\dfrac{360}{5.5} = \dfrac{720}{11} \approx 65.45$ minutes — so the hands meet 11 times in 12 hours (between 11 and 1 o’clock they meet only once, at 12:00).
In 24 hours: $2 \times 11 = 22$. (44 is the number of times they are at right angles.)
Answer: B