Directions, blood relations and Venn diagrams: previous-year questions
56 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 11 of them came in the last five papers.
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'A' started from his house and walked 20 m towards East, where his friend 'B' joined him. They together walked 10 m in the same direction. Then 'A' turned left while 'B' turned right and travelled 2 m and 8 m respectively. Again 'B' turned left to travel 4 m followed by 5 m to his right to reach his office. 'A' turned right and travelled 12 m to reach his office. What is the shortest distance between the two offices ?
Answer (b) & explanation
1. Draw it. Both reach a point 30 m east of A's house.
2. A: 2 m north, then 12 m east. B: 8 m south, 4 m east, then 5 m south.
3. Gap east–west: A went 12 m east, B 4 m east: 8 m. Gap north–south: A is 2 m north, B is 13 m south: 15 m.
4. 8 and 15 make a right-angled triangle: 8 × 8 + 15 × 15 = 64 + 225 = 289 = 17 × 17. Distance = 17 m.
Answer as per the official UPSC answer key.
A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D's father F. B and D are siblings and A is daughter of B. C is cousin of B. Who is E ?
- 1. Wife of F
- 2. Grandmother of A
- 3. Aunt of C
Select the correct answer using the code given below :
Answer (d) & explanation
E is F's wife, A's grandmother and C's aunt, so all three are right (d). Step 1: G is a widow and F's sister-in-law, so she is the wife of F's late brother. C, a cousin of B, is G's child. Step 2: there are three females: G, A (B's daughter) and one more. B and D's mother must be in the family, so E is F's wife. Step 3: then E is the grandmother of A, B's daughter. And E is C's aunt, as the wife of C's uncle F. Options (a), (b) and (c) leave out one true link.
Tip: draw a family tree with symbols (+ for male, − for female). Fix the widowed or married pairs first; the rest falls in place.
Answer as per the official UPSC answer key.
19 boys turn out for playing hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform?
Answer (c) & explanation
6 boys wear the full uniform (c). Step 1: 11 boys wear shirts and 14 wear pants. That adds to 25, but there are only 19 boys. Step 2: every boy wears at least one item, so the extra count comes from boys wearing both. Step 3: both = 11 + 14 − 19 = 6. Option (b), 5, and option (a), 3, undercount. Option (d), 8, overcounts.
Tip: this is the overlap rule for two groups: both = A + B − total, when no one is outside both groups. A quick Venn diagram makes it clear: 5 shirts only, 8 pants only, 6 both.
Answer as per the official UPSC answer key.
Lakshmi, her brother, her daughter and her son are badminton players. A game of doubles is about to begin :
- (i) Lakshmi's brother is directly across the net from her daughter.
- (ii) Her son is diagonally across the net from the worst player's sibling.
- (iii) The best player and the worst player are on the same side of the net.
Who is the best player?
Answer (a) & explanation
The best player is Lakshmi's brother (a). Step 1: by clue (i), the brother and the daughter are on opposite sides. Case 1: the brother partners Lakshmi. The son is diagonally across from the brother, whose sibling is Lakshmi. So Lakshmi is the worst player, and by clue (iii) the best is her partner, the brother. Step 2: case 2: the brother partners the son. The son is diagonal to the daughter, whose sibling is the son. So the son is the worst, and the best is his partner, the brother. Step 3: both cases give the brother. Options (b), (c) and (d) fail.
Tip: when a puzzle has two possible set-ups, try both. If they give the same answer, you are done.
Answer as per the official UPSC answer key.
Consider the following relationships among members of a family of six persons A, B, C, D, E and F :
- 1. The number of males equals that of females.
- 2. A and E are sons of F.
- 3. D is the mother of two, one boy and one girl.
- 4. B is the son of A.
- 5. There is only one married couple in the family at present.
Which one of the following inferences can be drawn from the above?
Answer (b) & explanation
A is the husband of D (b). Step 1: A and E are sons, and B is a son. So the males are A, E and B. Equal numbers means C, D and F are female. Step 2: A and E are F's sons, so F is their mother. D is the mother of one boy and one girl. D's son cannot be A or E, who are F's sons, so D's son is B. B is A's son, so D is A's wife. Step 3: C is their daughter. Since there is only one married couple, F is a widowed grandmother. Option (a) is wrong because A is male. Option (c) is wrong because E and F are not D's children. Option (d) has no support.
Tip: start with gender, then link parents and children.
Answer as per the official UPSC answer key.
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?
Answer (c) & explanation
Q is P's father (c). Step 1: "A + B" means A is the son of B. So P + R means P is the son of R. Step 2: "A − B" means A is the wife of B. So R − Q means R is the wife of Q. Step 3: R is P's mother, and Q is R's husband. So Q is P's father. Option (a), Q is P's son, reverses the relation. Option (b), Q is P's wife, is wrong because Q is R's husband. Option (d) fails because (c) is clear.
Tip: decode coded relations one pair at a time, left to right. Draw a small family tree as you go; it makes the final link easy to read.
Answer as per the official UPSC answer key.
A person X was driving in a place where all roads ran either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other in a parallel. He started at the intersection of two roads, drove 3 km north, 3 km west and 4 km south. Which further route could bring him back to his starting point, if the same route is not repeated ?
Answer (b) & explanation
He should go 3 km east, then 1 km north (b). Step 1: he goes 3 km north and then 4 km south. So he ends 1 km south of the start. He also went 3 km west. Step 2: to get back, he must go 3 km east and 1 km north. Step 3: check the "no repeat" rule. Going east along the road 1 km south of the start is a new road, then 1 km north brings him home. Option (a) takes him further south. Option (c) takes him further west. Option (d) leaves him 3 km south of where he started.
Tip: in direction problems, add up north–south and east–west moves separately. The net gap in each direction tells you the way home.
Answer as per the official UPSC answer key.
There are five persons in a group — P, Q, R, S and T. The group has one doctor, one lawyer and one artist. P and S are unmarried students. T is a man married to one of the group members. Q is the brother of P and is neither doctor nor artist. R is not doctor.
Who is the doctor ?
Answer (a) & explanation
T is the doctor (a). Step 1: P and S are students, so they have no jobs. The doctor, lawyer and artist must be Q, R and T. Step 2: Q is neither the doctor nor the artist, so Q is the lawyer. Step 3: R is not the doctor, so R is the artist. That leaves T as the doctor. Options (b) P and (d) R are ruled out above, and (c) Q is the lawyer.
Tip: in grid puzzles, first remove the people who cannot hold any job. Then use the "is not" clues one at a time. Each clue usually fixes one more person. Make a small table of names and jobs and cross out boxes as you go.
Answer as per the official UPSC answer key.
(Same information as the question above.)
Who is the artist ?
Answer (c) & explanation
R is the artist (c). Step 1: P and S are students, so the three jobs belong to Q, R and T. Step 2: Q is neither the doctor nor the artist, so Q is the lawyer. Step 3: R is not the doctor. The only job left for R is artist, and T is the doctor. So option (c) is right. Option (a) P is a student and has no job. Option (b) Q is the lawyer. Option (d) T is the doctor.
Tip: linked questions share one grid. Solve the grid fully once, then answer every question from it. This saves time and avoids answering the same puzzle in different ways.
Answer as per the official UPSC answer key.
(Same information as the question above.)
Who is the spouse of R ?
Answer (b) & explanation
R's spouse is T (b). Step 1: T is a man married to someone in the group. Step 2: P and S are unmarried students, so they cannot be T's spouse. Q is the brother of P, so Q is a man, and here the married couple is taken as a man and a woman. Step 3: that leaves R as T's wife. So R's spouse is T. Option (a) P and option (d) S are unmarried. Option (c) Q is a man and P's brother, so he is not the spouse.
Tip: relation clues like "brother" also tell you a person's gender. Note every such hint; it is often the key that settles a marriage question.
Answer as per the official UPSC answer key.
(Same information as the question above.)
Who is the lawyer ?
Answer (b) & explanation
Q is the lawyer (b). Step 1: the jobs are doctor, lawyer and artist. P and S are students, so the jobs belong to Q, R and T. Step 2: Q is neither doctor nor artist. The only job left for Q is lawyer. Step 3: check the rest. R is not the doctor, so R is the artist and T is the doctor. Option (a) P and option (d) S are students. Option (c) R is the artist.
Tip: a clue that rules out two of three choices fixes the third straight away. Look for such clues first. Here the clue about Q settles the lawyer before you need anything else.
Answer as per the official UPSC answer key.
(Same information as the question above.)
Who of the following is definitely a man ?
Answer (c) & explanation
Q is definitely a man (c). Step 1: the puzzle says Q is "the brother of P". A brother is male, so Q is certainly a man. Step 2: T is also described as a man. But T is not one of the options, apart from "None of the above", which is wrong because Q qualifies. Step 3: the genders of P and S are never given. P could be Q's brother or sister, and S could be either. So options (a) and (b) are not certain. Option (d) fails because Q is a man.
Tip: "definitely" means the facts must prove it. Do not assume gender from names, jobs or seating; only words like brother, wife or "a man" count.
Answer as per the official UPSC answer key.
A person climbs a hill in a straight path from point 'O' on the ground in the direction of north-east and reaches a point 'A' after travelling a distance of 5 km. Then, from the point 'A' he moves to point 'B' in the direction of north-west. Let the distance AB be 12 km. Now, how far is the person away from the starting point 'O' ?
Answer (b) & explanation
He is 13 km from the start (b). Step 1: north-east and north-west are at right angles to each other. So O, A and B form a right-angled triangle. Step 2: square the two short sides and add them: 5 × 5 + 12 × 12 = 25 + 144 = 169. Step 3: 13 × 13 = 169, so the distance OB is 13 km. Option (a), 7 km, is 12 − 5. Option (c), 17 km, is 12 + 5. Option (d), 11 km, does not fit.
Tip: learn the common right-triangle sets: 3-4-5, 5-12-13, 8-15-17 and 7-24-25. Seeing 5 and 12 should make you think of 13 at once.
Answer as per the official UPSC answer key.
A person walks 12 km due north, then 15 km due east, after that 19 km due west and then 15 km due south. How far is he from the starting point ?
Answer (a) & explanation
He is 5 km from the start (a). Step 1: north–south: 12 km north, then 15 km south, leaves him 3 km south of the start. Step 2: east–west: 15 km east, then 19 km west, leaves him 4 km west. Step 3: 3 km south and 4 km west form a right angle. The straight-line distance is √(3 × 3 + 4 × 4) = √25 = 5 km. Option (b), 9 km, does not fit. Option (c), 37 km, adds some of the walks. Option (d), 61 km, adds all four walks, which is total distance, not displacement.
Tip: "how far from the start" means straight-line distance. Cancel opposite directions first, then use the right-angle rule.
Answer as per the official UPSC answer key.
The number of persons who read magazine X only is thrice the number of persons who read magazine Y. The number of persons who read magazine Y only is thrice the number of persons who read magazine X. Then, which of the following conclusions can be drawn ?
- 1. The number of persons who read both the magazines is twice the number of persons who read only magazine X.
- 2. The total number of persons who read either one magazine or both the magazines is twice the number of persons who read both the magazines.
Select the correct answer using the code given below :
No official answer (question dropped) & notes
1. Call the readers of only X 'x', only Y 'y', and both 'b'. All Y readers = y + b; all X readers = x + b.
2. The facts say x = 3 × (y + b) and y = 3 × (x + b). So x is bigger than 3y, and y is bigger than 3x.
3. Both cannot be true at the same time for any real counts. The question has no valid answer as worded, which is why UPSC dropped it.
UPSC dropped this question from evaluation, so it has no official answer. It is printed here for practice only.
UPSC dropped this question from evaluation; there is no official answer.
Four persons A, B, C and D consisting of two married couples are in a group. Both the women are shorter than their respective husbands. A is the tallest among the four. C is taller than B. D is B's brother. In this context, which one of the following statements is not correct ?
Answer (c) & explanation
Statement (c) is not correct (c). Step 1: A is the tallest. Each wife is shorter than her husband, so the tallest person must be a husband: A is a man. D is B's brother, so D is also a man. Step 2: that leaves B and C as the two wives. Step 3: D cannot marry his own sister B, so the couples are A–B and D–C. Step 4: C is D's wife, so C is shorter than D. Option (c), "C is taller than D", is wrong. Check the others: (a) all are linked by family; (b) B is shorter than C, and C is shorter than her husband D and than A, so B is the shortest; (d) A is B's husband. These are correct.
Tip: in such puzzles, first fix who is a man and who is a woman, then pair the couples.
Answer as per the official UPSC answer key.
In a town, 45% population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine ?
Answer (c) & explanation
20% read no magazine (c). Step 1: use the three-set rule. Readers of at least one magazine = (A + B + C) − (each pair) + (all three). Step 2: A + B + C = 45 + 55 + 40 = 140. Pairs: 30 + 15 + 25 = 70. All three: 10. Step 3: at least one = 140 − 70 + 10 = 80%. Step 4: none = 100 − 80 = 20%. Options (a), (b) and (d) miss a step.
Tip: why add the "all three" back? When we subtract the pairs, people who read all three are taken away three times, after being added three times, so they vanish. Adding them once restores them. Draw a three-circle Venn diagram if unsure.
Answer as per the official UPSC answer key.
Shahid and Rohit start from the same point in opposite directions. After each 1 km, Shahid always turns left and Rohit always turns right. Which of the following statements is correct ?
Answer (b) & explanation
They meet after each has travelled 3 km (b). Step 1: Shahid walks north and Rohit south, in opposite directions. After 1 km, Shahid turns left (west) and Rohit turns right (also west, since he faces south). Step 2: after 2 km each, both have gone 1 km west. They are still 2 km apart (one north, one south of the start). So (a), saying 4 km, is wrong. Step 3: now Shahid turns left again, to south, and Rohit turns right again, to north. They walk toward each other and meet after 1 km more. Each has travelled 3 km. Options (c) and (d) are wrong.
Tip: draw the paths on paper. "Left" and "right" depend on which way a person is facing.
Answer as per the official UPSC answer key.
Out of 130 students appearing in an examination, 62 failed in English, 52 failed in Mathematics, whereas 24 failed in both English and Mathematics. The number of students who passed finally is
Answer (a) & explanation
40 students passed (a). Step 1: students who failed in at least one subject = English fails + Maths fails − both. That is 62 + 52 − 24 = 90. We subtract 24 because those students were counted in both 62 and 52. Step 2: students who passed both = 130 − 90 = 40. Options (b), (c) and (d) miss the overlap.
Tip: "passed finally" means passed both subjects. In two-set questions, always remove the double count: total in either = A + B − both. A two-circle diagram makes this clear.
Answer as per the official UPSC answer key.
In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group none can speak any other language. If 2 persons in the group can speak two languages only and one person can speak all the three languages, then how many persons are there in the group ?
Answer (c) & explanation
There are 23 persons (c). Step 1: add the language counts: 6 + 15 + 6 = 27. But this counts some people more than once. Step 2: each person who speaks two languages is counted twice, so is counted 1 extra time. There are 2 such persons: 2 extra counts. Step 3: the person who speaks all three is counted three times, so 2 extra counts. Step 4: people = 27 − 2 − 2 = 23. Options (a), (b) and (d) remove too much or too little.
Tip: think "extra counts". Someone in two groups adds one extra; someone in three groups adds two extra. Subtract all extras from the raw total.
Answer as per the official UPSC answer key.