Logical Reasoning Questions and Answers: 60 Solved Problems from Easy to Hard
This guide is for students and freshers preparing for the reasoning section of campus placement tests, off-campus drives and other aptitude exams in India. It covers 60 solved questions in three levels: the basic patterns and rules, the standard question types asked in most placement tests, and the longer puzzles and tricky conclusions that take the most time. Each answer explains the method step by step, so you can reuse it on new questions. Try each question first, then read the solution, and finish with the logical reasoning mock test.
- 60 questions, 3 levels
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What reasoning tests cover
- Series and patterns: number series, letter series, analogies and odd one out.
- Coding-decoding, blood relations, direction sense and ranking.
- Syllogisms and inequalities, where you decide which conclusions must follow.
- Arrangements and puzzles: linear and circular seating, ordering and scheduling puzzles.
- Clocks, calendars, cubes, Venn diagrams, critical reasoning (assumptions, arguments, conclusions) and data sufficiency.
How to prepare
- Learn the letter positions (A = 1 to Z = 26) and their reverse positions. The pairs E-5, J-10, O-15, T-20 and Y-25 help you count quickly.
- Always draw: a family tree for blood relations, arrows for directions, a row of boxes for seating, and circles for syllogisms.
- Practise puzzles under a timer. They carry several questions each, so solving one well pays off several times.
- Review wrong answers carefully. In reasoning, most mistakes come from misreading a single word such as "only", "immediate" or "not".
Strategy on test day
- Start with quick types (series, coding, directions, inequalities) to bank marks, then move to puzzles.
- In a puzzle, write down the fixed clues first and then the conditional ones.
- For syllogisms and conclusions, use only the information given, never your general knowledge.
- If a puzzle has two possible arrangements after 3 minutes, move on and come back with fresh eyes.
Logical Reasoning interview questions: Easy questions
20 questions1. How do you approach a number series question?
First check the differences between terms. If they are equal, it is an arithmetic series. If the differences themselves change steadily (for example 2, 4, 6), look at the second differences. Then check for multiplication (x2, x3), squares and cubes (1, 4, 9, 16 or 1, 8, 27), and two alternating series. For 3, 7, 13, 21, 31, ?: the differences are 4, 6, 8, 10, so the next difference is 12 and the answer is 43.
2. What is a quick way to remember letter positions?
Remember EJOTY: E = 5, J = 10, O = 15, T = 20, Y = 25. Any letter is then a step or two away from one of these, for example R = 18 (T minus 2). The reverse position of a letter is 27 minus its position, so the opposite of D (4) is W (23). Pairs like A-Z and B-Y always add up to 27.
3. If CAT is written as DBU, how is DOG written?
Compare each letter: C to D, A to B and T to U, so every letter moves one place forward. Apply the same rule to DOG: D to E, O to P and G to H, giving EPH. In coding questions, write the letter positions above the word and look for a constant shift, a reversal or an opposite-letter rule.
4. If A is the brother of B and B is the sister of C, how is A related to C?
A, B and C are siblings. A is male (a brother), so A is the brother of C. C's gender is not given, but that does not change the answer. In blood relation questions, mark each person's gender only when the question tells you, and do not assume it from the relation of others.
5. What are the basic rules for direction sense questions?
Draw a cross with North at the top. A right turn while facing North makes you face East, and a left turn makes you face West. Track the facing after every turn. For distance from the start, add up all East-West movement and all North-South movement separately; if both are non-zero, use Pythagoras. Walking 3 km North and then 4 km East leaves you 5 km from the start, towards the North-East.
6. In a row, Ravi is 7th from the left and 12th from the right. How many people are in the row?
Total = position from left + position from right - 1 = 7 + 12 - 1 = 18. You subtract 1 because Ravi is counted in both positions. If you are given the total and one position, rearrange it: position from right = total - position from left + 1.
7. How do you find the odd one out among numbers?
Check common properties in order: even or odd, prime, perfect square, perfect cube, multiple of a number, and digit sum. In 25, 36, 49, 63, 81, all are perfect squares except 63, so 63 is the odd one. Good questions have exactly one number that breaks the pattern; if two seem odd, look for a second property that settles it.
8. How do you solve an analogy such as 3 : 27 :: 5 : ?
Find how the first pair is related and apply the same rule to the second. 27 = 3^3, so the rule is "cube the number", and 5^3 = 125. Other common rules are squaring, n^2 + 1, n(n + 1), multiplying by a fixed number and letter shifts. Always check that the rule works for the given pair before using it.
9. What is the formula for the angle between the hands of a clock?
Angle = |30H - 5.5M| degrees, where H is the hour and M the minutes. If the result is more than 180, subtract it from 360 to get the smaller angle. At 3:40, the angle is |90 - 220| = 130 degrees. The formula works because the hour hand moves 0.5 degrees a minute and the minute hand 6 degrees a minute.
10. If today is Monday, what day will it be after 45 days?
Days repeat every 7, so only the remainder matters: 45 = 7 x 6 + 3. Move 3 days forward from Monday: Tuesday, Wednesday, Thursday. The answer is Thursday. These leftover days are called odd days, and they are the basis of every calendar question.
11. In a group of 60, 35 like tea, 30 like coffee and 15 like both. How many like neither?
Use the formula: at least one = tea + coffee - both = 35 + 30 - 15 = 50. Neither = 60 - 50 = 10. The "both" group is subtracted once because it was counted in tea and in coffee. Drawing two overlapping circles makes this obvious.
12. A cube painted on all faces is cut into 27 equal small cubes. How many have exactly two faces painted?
With 27 cubes, there are 3 along each edge (n = 3). Cubes with two painted faces sit along the edges but not at the corners: 12 edges x (n - 2) = 12 x 1 = 12. The other formulas: three faces = 8 (the corners), one face = 6(n - 2)^2 = 6, and no face = (n - 2)^3 = 1.
13. How do you check a syllogism such as "All pens are books. All books are bags. Conclusion: All pens are bags."?
Draw circles: pens inside books, and books inside bags. Then pens must be inside bags, so the conclusion follows. A conclusion follows only if it is true in every possible diagram of the statements. For "some" statements, draw the smallest overlap that the statement allows, then test the conclusion.
14. Given A > B = C >= D, is A > D true?
Follow the chain from A to D: A > B, B = C and C >= D. Every sign points the same way, and there is at least one strict sign (>), so A > D is definitely true. If the signs point in opposite directions anywhere on the path, such as A > B < C, no relation can be concluded.
15. In seating questions where people face north, which side is left?
When people sit in a row facing north, their left is your left as you look at the diagram from behind them, so the left end of the drawn row is their left. When people face south (towards you), their left and right are reversed compared with yours. Always write the facing direction at the top of your diagram before placing anyone.
16. P is taller than Q, R is shorter than Q, and S is taller than P. Who is the shortest?
Build one chain: S > P (S is taller than P), P > Q and Q > R. So S > P > Q > R, and R is the shortest. In ordering puzzles, convert every sentence into the same symbol, here ">" meaning taller, before you combine them.
17. What is the difference between a conclusion and an assumption?
A conclusion is something that follows from the statement. An assumption is something the author takes for granted without saying it. For "Use our app to save time on bills", an assumption is that people want to save time. A conclusion might be that the app offers bill payment. In tests, an implicit assumption must be necessary for the statement to make sense.
18. What do the standard answer choices in data sufficiency questions mean?
You decide whether the given statements are enough to answer the question, not what the answer is. Typical choices are: statement I alone is enough; statement II alone is enough; either one alone is enough; both are needed together; or both together are still not enough. Test each statement on its own first, and only then combine them.
19. How do you solve a letter series like B, E, H, K, ?
Convert to positions: B = 2, E = 5, H = 8, K = 11. The gap is 3 each time, so the next is 14 = N. If the gaps change, track them as you would in a number series. For pairs such as AZ, BY, CX, look at each letter of the pair separately: the first goes forward and the second goes backward.
20. How do you solve a coding question where words are coded by letter positions?
Check whether the code is the sum, product or list of letter positions. If CAB is coded as 6 (3 + 1 + 2), then the code is the sum of positions, so BAD = 2 + 1 + 4 = 7. Another common pattern is position multiplied by a fixed number. Test the rule on the example before applying it to the new word.
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Logical Reasoning interview questions: Medium questions
20 questions21. How do you spot two alternating series hidden in one?
If the differences jump around with no pattern, split the series into odd and even positions. In 2, 20, 4, 17, 6, 14, ?, the odd positions go 2, 4, 6 (adding 2) and the even positions go 20, 17, 14 (subtracting 3). The next term is in an odd position, so it is 8. Alternating series are common when a series has 7 or more terms.
22. What comes next in 2, 6, 12, 20, 30, ?
The differences are 4, 6, 8, 10, so the next difference is 12 and the answer is 42. The terms also follow n(n + 1): 1 x 2, 2 x 3, 3 x 4, 4 x 5, 5 x 6, 6 x 7 = 42. Recognising standard forms like n(n + 1), n^2 + 1 and n^3 - 1 lets you answer without computing differences.
23. If GARDEN is coded as NEDRAG, how is MARKET coded?
NEDRAG is GARDEN written backwards, so the rule is to reverse the word. MARKET reversed is TEKRAM. Some questions combine reversal with a shift, for example reversing and then moving each letter one place forward, so always check both steps on the example.
24. If P + Q means P is the father of Q and P x Q means P is the sister of Q, what does A + B x C mean?
Read from left to right: A + B means A is the father of B, and B x C means B is the sister of C. So B and C are siblings, and A is the father of both. A + B x C means A is the father of C. In coded relations, translate one symbol at a time and draw the tree as you go.
25. Pointing to a man, Rita says, "His mother is the only daughter of my mother." How is Rita related to the man?
Rita is a daughter of her own mother. If her mother has only one daughter, that daughter is Rita. So Rita is the man's mother. Phrases such as "only daughter" or "only son" usually point back to the speaker; check that possibility first.
26. In the morning, Raj walks towards the sun and his shadow falls behind him. He then turns left. Which direction is he facing?
In the morning the sun is in the East, so Raj is walking East. Turning left from East makes him face North. Shadow questions rely on two facts: the morning sun is in the East (shadows fall West) and the evening sun is in the West (shadows fall East). At noon, there is almost no shadow.
27. How many times do the hands of a clock overlap in a day?
They overlap 11 times in every 12 hours, not 12, because the overlap between 11 and 1 o'clock happens only once, at 12:00. In 24 hours they overlap 22 times. Similarly, the hands are at right angles 44 times a day and point in opposite directions 22 times a day.
28. Which years are leap years?
A year is a leap year if it is divisible by 4, except century years, which must be divisible by 400. So 2024 and 2000 are leap years, but 1900 and 2100 are not. A normal year has 1 odd day (365 = 52 weeks + 1 day) and a leap year has 2. This is why the same date moves forward by one weekday each year, or by two after 29 February.
29. Statements: "Some cats are dogs. All dogs are birds." Does "Some cats are birds" follow?
Yes. The cats that are dogs are inside the dogs circle, and the whole dogs circle is inside birds, so those cats are also birds. Therefore "Some cats are birds" is definitely true. But "All cats are birds" does not follow, because other cats may be outside the dogs circle.
30. When is the answer to a syllogism "Either I or II follows"?
When neither conclusion is certain on its own, but together they cover every possibility about the same two groups. The common pairs are "Some A are B" with "No A are B", and "All A are B" with "Some A are not B". If one of the pair definitely follows, choose that one instead of "either".
31. Given P >= Q = R and conclusions I: P > R and II: P = R, which follows?
From the chain, P >= R: P is either greater than or equal to R, but we do not know which. Neither conclusion is certain alone, but together they cover both cases, and they compare the same two letters. So the answer is "Either I or II is true". This is the most common either-or case in inequalities.
32. How do circular seating arrangements differ from linear ones?
In a circle, nobody sits at an end, so start by fixing one person and placing others relative to them. When people face the centre, their right is the anticlockwise direction and their left is clockwise as you look down on the circle. If some face outward, their left and right swap. Count "second to the left" by skipping one seat in the correct direction.
33. How do you solve a puzzle where five people have different jobs and live on different floors?
Make a grid with floors as rows and columns for the person and the job. Fill in definite clues first, such as "A lives on the top floor". Then use clues that limit positions, such as "B lives just above C", to list the possible cases. Eliminate cases that break a later clue. Puzzles are designed so that exactly one case survives.
34. Statement: "The government should reduce taxes on electric cars to cut pollution." Is the assumption "Electric cars pollute less than petrol cars" implicit?
Yes. The suggestion only makes sense if electric cars pollute less; otherwise encouraging them would not cut pollution. A good test: if negating the assumption (electric cars pollute just as much) makes the statement pointless, the assumption is implicit.
35. How do you weaken an argument in critical reasoning questions?
Find the gap between the evidence and the conclusion, then choose the option that attacks that link. If an argument says "Sales rose after the ad campaign, so the campaign worked", a weakening option would be "A rival brand shut down the same month", because it gives another reason for the rise. Options that are merely negative about the topic, without touching the link, do not weaken it.
36. Is x > 0? I. x^2 = 16. II. x^3 = 64. Which statement is sufficient?
Statement I gives x = 4 or x = -4, so it cannot tell whether x is positive. Statement II gives x = 4 only, because a cube keeps the sign. So statement II alone is sufficient. In data sufficiency, always check for negative values, zero and non-integers before deciding that a statement is enough.
37. In a class, A is 10th from the top. B is 5 ranks below A and 20th from the bottom. How many students are in the class?
B is 10 + 5 = 15th from the top and 20th from the bottom. Total = 15 + 20 - 1 = 34. Ranking questions with more than one person become simple once you find one person's position from both ends.
38. Out of 100 students, 50 study Hindi, 40 study English and 30 study Sanskrit. 15 study Hindi and English, 10 study English and Sanskrit, 12 study Hindi and Sanskrit, and 5 study all three. How many study none?
At least one = H + E + S - (HE + ES + HS) + all three = 50 + 40 + 30 - (15 + 10 + 12) + 5 = 120 - 37 + 5 = 88. None = 100 - 88 = 12. The "all three" group is added back because it was subtracted three times in the pairwise overlaps.
39. A cube is painted red on two opposite faces, blue on two others and green on the last two, then cut into 64 equal cubes. How many small cubes have no paint?
With 64 cubes there are 4 along each edge. Cubes with no paint are the inner ones: (4 - 2)^3 = 8. The colours do not matter for this question. They matter only when the question asks about specific colour combinations, such as cubes with both red and green.
40. Find the odd one out: 121, 144, 169, 196, 225, 250.
121, 144, 169, 196 and 225 are the squares of 11, 12, 13, 14 and 15. 250 is not a perfect square, so it is the odd one. When numbers are large, check whether they are squares or cubes of consecutive numbers before trying more complicated rules.
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Logical Reasoning interview questions: Hard questions
20 questions41. Find the wrong number in the series: 2, 5, 11, 23, 48, 95.
Each term is double the previous plus 1: 2, then 5, 11, 23, 47, 95. So 48 is wrong and should be 47. In "wrong number" questions, find the rule from the terms that fit, then check every term against it; the correct series will have exactly one term that breaks the rule.
42. If each letter in a word moves forward by its position number (1st letter by 1, 2nd by 2 and so on), how is MATH coded?
M moves 1 to N, A moves 2 to C, T moves 3 to W, and H moves 4 to L. So MATH becomes NCWL. Position-based shifts look random at first; compare the shift for each letter (1, 2, 3, 4) to see that it grows with the position.
43. A is the mother of B. B is the sister of C. D is the son of C. E is the brother of D. F is the mother of E. G is A's husband. How is F related to G?
D and E are brothers, and F is their mother. Their other parent is C, who must then be their father, so F is C's wife. C is a child of A and G. So F is G's daughter-in-law. In long blood relation chains, draw the tree with generations in rows and mark gender only when it is stated or forced.
44. A man walks 10 m North, turns right and walks 6 m, turns right and walks 18 m, then turns left and walks 9 m. How far and in which direction is he from the start?
North 10, then East 6, then South 18, then East 9. Net: East 6 + 9 = 15 m, and North 10 - 18 = 8 m South. Distance = sqrt(15^2 + 8^2) = sqrt(289) = 17 m, towards the South-East. Writing each move as East-West and North-South numbers avoids errors in long paths.
45. A clock gains 5 minutes every hour. It is set right at 8:00 am. What time does it show at 8:00 pm the same day?
From 8 am to 8 pm is 12 hours, so the clock gains 12 x 5 = 60 minutes and shows 9:00 pm. If asked the reverse, when the clock shows 9:00 pm what is the real time, you would work back from the clock's rate: the clock runs 65 minutes for every 60 real minutes.
46. What time does a clock's mirror image show when the actual time is 3:20?
For a mirror image, subtract the time from 11:60. 11:60 - 3:20 = 8:40, so the mirror shows 8:40. If the hours are 11 or 12, subtract from 23:60 instead. For a water image (reflection from below), the rule is different, so read the question carefully.
47. What day of the week was 15 August 1947?
It was a Friday. To work it out: 1600 years give 0 odd days and 300 years give 1 (each 100 years gives 5, and 3 x 5 = 15, which leaves 1). The 46 years from 1901 to 1946 include 11 leap years, giving 46 + 11 = 57, or 1 odd day. From 1 January to 15 August 1947 there are 227 days, which leave 3 odd days. The total is 0 + 1 + 1 + 3 = 5 odd days, and counting from Sunday as 0, 5 is Friday.
48. Statements: "No man is a woman. Some women are doctors." Conclusions: I. Some doctors are not men. II. No doctor is a man. Which follows?
The doctors who are women cannot be men, because no woman is a man, so I definitely follows. II does not follow: other doctors may be men. The answer is "Only I follows". Look for "some ... not" conclusions after a "no" statement. They often follow when a "some" statement connects the groups.
49. Statements: "All phones are tablets. Some tablets are laptops." Conclusion: "Some phones are laptops" is a possibility. Does it follow?
Yes. Nothing stops some phones from being among the tablets that are laptops, so it is possible. "Possibility" conclusions follow unless they contradict a statement. A possibility of "All tablets are phones" would also follow, but a possibility that some phones are not tablets would not, because all phones are tablets.
50. Statements: A > B, B >= C, C = D, D < E. Conclusions: I. A > D. II. E > B. Which is true?
A > B >= C = D gives A > D, so I is true. For II, the path from E to B is E > D = C <= B: the signs point in opposite directions at C and B, so no relation can be derived, and II is not certain. The answer is "Only I is true". When combining several statements, write them into one chain first.
51. Eight people sit around a square table, two on each side, all facing the centre. A sits second to the right of B. C is opposite A. If B sits at a corner position, where is C relative to B?
Fix B and count two seats anticlockwise (right, when facing the centre) to place A. C is directly opposite A, four seats away around the table. So C is two seats to B's left, counting clockwise. In square and circular tables with 8 seats, "opposite" always means four seats away in either direction.
52. Seven lectures, P to V, are scheduled on seven days from Monday to Sunday. R is on Wednesday. Two lectures fall between R and T. P is just before Q. V is on the last day. Which day is T?
Two lectures between R (Wednesday) and T means T is three days after Wednesday (Saturday), because three days before Wednesday falls outside the week. So T is on Saturday, and V takes Sunday. Scheduling puzzles become easier when you place the fixed days first (R and V), then the clues with a gap, then the "just before" pairs.
53. An input-output machine turns "sky 42 ant 17 dog 35" into "ant 17 sky 42 dog 35" in step I. What is it most likely doing?
Look for one element moved per step. Here "ant", the first word alphabetically, moved to the front together with the number after it. Machine-input questions usually sort words alphabetically and numbers by size, one per step. Find the rule from the first two steps, then apply it to the new input.
54. Argument: "Students who take coaching score higher, so coaching improves scores." What is the flaw?
It confuses correlation with causation. Students who take coaching may already be more motivated or have more resources, and that may explain the higher scores. A strong study would compare similar students, ideally assigned at random. In critical reasoning, ask whether another factor could explain both things.
55. Statement: "Many people in the city fell ill after drinking tap water." Course of action: I. Test the water supply immediately. II. Ban all water supply in the city. Which should be followed?
Only I. Testing addresses the problem directly and is practical. Banning all water supply would cause greater harm and is an extreme step. A good course of action is practical, addresses the problem and does not create a bigger one.
56. Is x > y? I. x/y > 1. II. y > 0. Which statements are needed?
Statement I alone fails: if both are negative, for example x = -4 and y = -2, then x/y = 2 > 1 but x < y. Statement II alone says nothing about x. Together: if y > 0, multiplying x/y > 1 by y keeps the sign, so x > y. Both statements are needed. The sign of what you multiply or divide by is the classic trap in inequalities.
57. What is the two-digit number? I. The sum of the digits is 11. II. Reversing the digits increases the number by 27.
Statement I alone allows 29, 38, 47 and so on. Statement II alone gives (10u + t) - (10t + u) = 27, so u - t = 3, which allows 14, 25, 36 and so on. Together, t + u = 11 and u - t = 3 give u = 7 and t = 4, so the number is 47. Both statements are needed.
58. In a row of 40 students, A is 12th from the left. After A and B swap places, A becomes 25th from the left. What is B's position from the right?
After the swap, A is in B's old place, so B was 25th from the left. Before the swap, B's position from the right was 40 - 25 + 1 = 16. After the swap, B is in A's old place, 12th from the left, which is 40 - 12 + 1 = 29th from the right. Make sure you know whether the question asks about the position before or after the swap.
59. In a class of 50, 30 play cricket, 25 play football and 10 play neither. How many play only one game?
At least one = 50 - 10 = 40. Both = 30 + 25 - 40 = 15. Only cricket = 30 - 15 = 15 and only football = 25 - 15 = 10. Only one game = 15 + 10 = 25. Questions about "only" regions need the "both" figure first.
60. Four positions of a die show 1 next to 2, 3, 4 and 5. Which number is opposite 1?
On a die, a face is adjacent to four faces and opposite one. If 2, 3, 4 and 5 all appear next to 1, the only number left, 6, must be opposite 1. This elimination rule is the fastest way to solve most dice questions: list everything adjacent to a face, and the missing number is opposite.
Practice questions for November 2026
New every month3 questions from the Logical Reasoning mock test, the way they appear in it. A new set comes on the 1st of every month. Pick your answer, then open it.
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What is the smaller angle between the hour and minute hands of a clock at 10:45?
- 42.5 degrees
- 67.5 degrees
- 52.5 degrees
- 30 degrees
Show the answer
Answer: 52.5 degrees. Angle = |30H - 5.5M| = |30 x 10 - 5.5 x 45| = 52.5. The smaller angle is 52.5 degrees.
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What is the value of x + y? I. 2x + 2y = 18. II. x - y = 3.
- Either statement alone is sufficient
- Statement I alone is sufficient
- Both statements together are needed
- Statement II alone is sufficient
Show the answer
Answer: Statement I alone is sufficient. I gives x + y = 9 directly. II alone gives only the difference.
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Argument: 'Our sales fell after we raised prices by 5 percent, so we should cut prices by 10 percent to double our sales.' Which assumption does this rely on?
- Competitors will raise their prices
- Costs will fall by 10 percent
- Customers did not notice the price rise
- Sales respond to price in a simple, proportional way
Show the answer
Answer: Sales respond to price in a simple, proportional way. The argument assumes a linear link between price and sales, which is rarely true.
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