Ranking and ordering is 67 of the 692 reasoning questions the Punjab Police SI has asked, and it is the topic where the idea is easy and the execution decides everything. Nobody fails to understand that if A is taller than B and B is taller than C then A is taller than C. People fail because they compare a position counted from the left with a position counted from the right, or because they read “only three are younger” from the wrong end. The 67 fall into three kinds. 28 give you comparisons in words and ask you to build the order. 26 place someone in a row and ask where they stand. 13 give one person's rank from both ends and ask for the total. Each kind has exactly one rule, and all three rules are one line long.
The teaching part above and below — the explanations, the figures and the worked examples on screen — is about 19 minutes. The collapsed question banks hold 67 solved past questions in all; working through every one of them takes roughly 2 hours. Do that across several sittings, not in one go.
- Position from left + position from right = total + 1.
- Total = rank from one end + rank from the other end − 1, when both ranks belong to the same person.
- “Only k are above X” puts X at place k + 1 from the top.
- Comparing a left position with a right position.
- Adding the two ranks and forgetting the −1.
- Reading “only” from the wrong end of the order.
Part 1 · Position in a row — 26 questions
Convert both positions to the same end before anything else
Nearly every one of these twenty-six hands you two facts measured from different ends — “Payal is 4th from the right and Raman is 12th from the left” — and then asks how many people sit between them. The numbers 4 and 12 cannot be subtracted, because they are counted in opposite directions. So the first line you write is a conversion. In a row of n people, position from the left = n + 1 − position from the right, and the same formula works the other way. Once both are measured from the same end, every question in this part is one subtraction.
If two people stand at places 7 and 15 from the same end, the number of people between them is 15 − 7 − 1 = 7, while the number of places from one to the other is 15 − 7 = 8. Both are asked, and the options always contain both answers. Underline the word “between” when you see it.
Some questions say the row faces north or south. That decides which end is somebody's right. Facing north, a person's right hand points east; facing south, it points west. Mark the direction on your sketch before you number the seats, and a “fourth to the right of S” stops being ambiguous.
Every other position-in-a-row question (20)Tap to open
In a row of girls, Chetna is 7^{th} from the right and Neelam is 15^{th} from the left. If both of them exchange their positions, then Chetna becomes 20^{th} from the right. How many girls are there in the row ? (SI 2016)
- 126
- 221
- 335
- 434
Show answer
Answer: 4 — 34
After the exchange Chetna stands exactly where Neelam stood, i.e. 15th from the left, and we are told that same place is 20th from the right. For any single position in a row, (rank from left) + (rank from right) − 1 = total. So total = 15 + 20 − 1 = 34. Chetna's original 7th-from-right is only there to mislead: it is not needed, and using it (7 + 20 − 1 = 26) gives option 1, the classic trap.
In a row of boys facing North, Samit is 5^{th} to the left of Sumit, Savit is 3^{rd} to the right of Samit. Samvit is 3^{rd} to the left of Sumit. Which of the following describes the position of Samvit? (SI 18 Aug 2021)
- 1To the immediate right of Savit
- 23^{rd} to the right of Samit
- 3To the immediate left of Savit
- 4To the immediate right of Samit
Show answer
Answer: 3 — To the immediate left of Savit
Number the places along the row so that moving right adds 1 and moving left subtracts 1, and anchor everything to Sumit at 0. Samit is 5th to Sumit's left, so Samit = −5. Savit is 3rd to Samit's right, so Savit = −5 + 3 = −2. Samvit is 3rd to Sumit's left, so Samvit = −3. Samvit at −3 sits one place to the left of Savit at −2, so Samvit is immediately to Savit's left. Option 1 reverses that and would put Samvit at −1. Option 2 describes −2, which is Savit's own place, not Samvit's. Option 4 describes −4, one place right of Samit, which is empty of the named boys. The order along the row is Samit, _, Samvit, Savit, _, Sumit.
In a row, Lily is at the eighteenth place from the front while Mini is at the sixteenth place from the back. If Nisha is at the twenty-fifth place from the front and is at exactly the middle place between Lily and Mini, then how many people are there in the row? (SI 19 Aug 2021)
- 147
- 244
- 348
- 445
Show answer
Answer: 1 — 47
Count every position from the front. Lily stands at 18 and Nisha at 25, so Nisha is 25 − 18 = 7 places behind Lily. Being exactly midway between Lily and Mini, Nisha must also be 7 places ahead of Mini, which puts Mini at 25 + 7 = 32 from the front. Mini is also 16th from the back, and for any person the two counts overlap on that person, so the total is (place from front) + (place from back) − 1 = 32 + 16 − 1 = 47. Option 3 (48) is what you get by forgetting to subtract the 1 for double-counting Mini herself, and option 4 (45) by taking Nisha rather than Mini as the reference.
Suman is the 22nd player in a row all facing north. Sanjay, who is fifteenth from the left end of the row, is fifth to the left of Suman. If Suman is shifted to her right by four places she becomes eighteenth from the right end of the row. How many players are there in the row? (SI 20 Aug 2021)
- 142
- 241
- 339
- 438
Show answer
Answer: 2 — 41
Sanjay is 15th from the left and stands five places to Suman's left, so Suman is 15 + 5 = 20th from the left end. (Her stated rank of 22 is therefore counted from the right end, which is the consistency check for the whole problem.) Move Suman four places to her right: she becomes 20 + 4 = 24th from the left, and she is then 18th from the right. In a row, position from left + position from right − 1 = total, so total = 24 + 18 − 1 = 41. Cross-check with her original rank: 20th from the left in a row of 41 makes her 41 − 20 + 1 = 22nd from the right, exactly as stated. Option 1 (42) is the classic error of forgetting to subtract the one place counted twice.
There are 23 students in a yoga class, and the trainer is planning for an arrangement of students on stage on the occasion of International Yoga Day. Rupak is 10th from the left side of the row and Raghu is 21st from the right side of the row. Find the number of students sitting between Rupak and Raghu. (SI 20 Jun 2023)
- 18
- 25
- 37
- 46
Show answer
Answer: 4 — 6
Convert Raghu's position to the same end. Position from left = total − position from right + 1 = 23 − 21 + 1 = 3. So Raghu is 3rd from the left and Rupak is 10th from the left. The number strictly between two positions is the difference minus one: 10 − 3 − 1 = 6. Option 3 (7) is what you get if you forget to subtract the 1 and count one of them as well.
Some persons are sitting in a row facing north. Exactly seven persons sit between P and S. T sits fourth to the right of S. Q sits third to the left of S. P sits third to the right of R. T and R sit at the corner positions of the row. If no other person is sitting in the row, how many persons in total are sitting in the row? (SI 21 Jun 2023)
- 116
- 217
- 314
- 415
Show answer
Answer: 1 — 16
Number the seats from left to right and put S at seat s. T is fourth to the right of S, so T = s+4; Q is third to the left of S, so Q = s−3. Seven persons between P and S means P is eight seats away, so P = s+8 or P = s−8. If P = s+8, then R = P−3 = s+5, and both T (s+4) and R (s+5) would have to be the two ends while P sits beyond them at s+8 — impossible. So P = s−8 and R = P−3 = s−11. Now R at s−11 is the leftmost seat and T at s+4 is the rightmost, which matches the corner condition. Total = (s+4) − (s−11) + 1 = 16. The common slip is taking 'seven persons between' as a gap of seven seats, which gives 15.
Some persons are sitting in a row facing north. B sits at one of the ends of the row. G sits second to the right of L. M sits sixth to the left of G. Exactly two persons sit between B and M. If no other person sits in the row, then what will be the total number of persons sitting in the row? (SI 1 Jul 2023)
- 113
- 210
- 311
- 412
Show answer
Answer: 2 — 10
All face north, so each person's right is towards the east end. Number the seats 1 … n from the west (left) end. - G is second to the right of L → G = L + 2. - M is sixth to the left of G → M = G − 6, so M = L − 4. - Exactly two persons between B and M → B and M are 3 seats apart. B is at an end. If B were to the east of M, B = M + 3, but G = M + 6 sits further east still, so B could not be the end — rejected. So B is to the west of M: B = M − 3, and B is the west end, seat 1. Then M = 4, L = 8 and G = 10, and nobody sits beyond G. ```puzzle:row row (N): B, ?, ?, M, ?, ?, ?, L, ?, G ``` Total = 10. Option 4 (12) comes from counting B and M as "two persons between" rather than the two seats strictly between them.
In a row of people standing facing north, Rajpal is standing at the 7th position from the right end. Seema is standing at the 15th position from the right end. Seema is standing exactly in the middle of Rajpal and Teena. If Teena is standing at the 10th position from the left end of the row, then how many persons in total are there in the row? (SI 1 Jul 2023)
- 134
- 232
- 331
- 433
Show answer
Answer: 2 — 32
Count everything from the right end first. - Rajpal = 7th from the right. - Seema = 15th from the right, so Seema is 15 − 7 = 8 places from Rajpal. - Seema is exactly midway between Rajpal and Teena, so Teena is another 8 places beyond Seema: 15 + 8 = 23rd from the right. Teena is also 10th from the left, so Total = (position from left) + (position from right) − 1 = 10 + 23 − 1 = 32. The usual slip is forgetting the −1 (which gives 33, option 4) — Teena must not be counted twice.
70 cars are arranged in a straight line from left to right. Vatsala's car was at the 27th position from the left end. What will be its position from the right end? (SI 2 Jul 2023)
- 144th
- 245th
- 342nd
- 443rd
Show answer
Answer: 1 — 44th
For one row, position from left + position from right = total + 1. So position from right = 70 − 27 + 1 = 44. The classic slip is to forget the +1 and answer 43 (option 4).
Thirty-three students are sitting in a row. Shubham is twenty-forth from the right. Manish is twelfth from the left. How many students are there between Shubham and Manish? (SI 3 Jul 2023)
- 12
- 24
- 33
- 41
Show answer
Answer: 4 — 1
Convert both positions to the same end. Position from the left = total − position from the right + 1, so Shubham = 33 − 24 + 1 = 10th from the left. Manish is 12th from the left. The number strictly between two positions is (larger − smaller − 1) = 12 − 10 − 1 = 1, namely the student at seat 11. The common slip is to answer 2 by subtracting 10 from 12 without dropping the endpoint.
In a row of people all facing north, Saina is 5^th from the right end. Prayag is 15^th from the right end. Prayag is exactly between Saina and Ria. If Ria is 5^th from the left end of the row, then how many people in total are there in the row? (SI 3 Jul 2023)
- 130
- 229
- 332
- 431
Show answer
Answer: 2 — 29
Work entirely from the right end. Saina is at 5 and Prayag at 15, so Prayag stands 15 − 5 = 10 places to the left of Saina. 'Exactly between Saina and Ria' means Prayag is the midpoint, so Ria must be another 10 places further left: Ria is 15 + 10 = 25th from the right end. Ria is also 5th from the left, so total = 25 + 5 − 1 = 29, subtracting one because Ria is counted from both ends. Forgetting that overlap gives 30, the first distractor.
Each one out of P, Q, R, S, T and U is of a different age. P is the oldest and U is the youngest. S is older than 2 friends only. How many friends have their ages between P and S? (SI 3 Jul 2023)
- 14
- 22
- 31
- 43
Show answer
Answer: 2 — 2
Line the six up from oldest (place 1) to youngest (place 6). P takes place 1 and U place 6. 'S is older than 2 friends only' means exactly two people sit below S, so S takes place 4 (places 5 and 6 are below it). Between place 1 (P) and place 4 (S) lie places 2 and 3 — two friends. Answering 3 counts S itself, and answering 4 counts the whole gap down to U.
Rohan is 21^{st} from both the ends of the row of students of class 11. How many students are there in the row? (SI 9 Jul 2023)
- 143
- 232
- 341
- 442
Show answer
Answer: 3 — 41
When one person's position is given from both ends, the total is (position from left) + (position from right) − 1, the −1 removing the double count of that person. Here the total is 21 + 21 − 1 = 41. Option 4 (42) is the answer you get by forgetting to subtract the person counted twice.
Raj and Vihan are standing in a row of 49 boys facing the north. Raj is standing seventh to the left of Vihan, who is standing twelfth from the right. What is Raj’s position from the left? (SI 9 Jul 2023)
- 131st
- 220th
- 322nd
- 419th
Show answer
Answer: 1 — 31st
First convert Vihan's position. He is twelfth from the right in a row of 49, so from the left he is 49 − 12 + 1 = 38th. Raj stands seventh to the left of Vihan, so Raj's position from the left is 38 − 7 = 31st. Option 4 (19th) comes from subtracting seven from twelve and working from the wrong end.
In a row of people all facing north, Julie is 6^{th} from the right end. Alex is 18^{th} from the right end. Alex is exactly between Rohan and Julie. If Rohan is 5^{th} from the left end of the row, then how many people in total are there in the row? (SI 14 Jul 2023)
- 133
- 235
- 332
- 434
Show answer
Answer: 4 — 34
Count everything from the right end first. Julie is 6th from the right; Alex is 18th from the right. The gap between them is 18 − 6 = 12 places. 'Alex is exactly between Rohan and Julie' means Alex is the midpoint, so Rohan must be the same 12 places further from the right: 18 + 12 = 30th from the right. Rohan is also 5th from the left, so the total is (position from left) + (position from right) − 1 = 5 + 30 − 1 = 34. The near miss 33 comes from forgetting to subtract the double-counted person, and 35 from adding one instead.
In a row of 48 officers facing the North, Nirupaman is 6th to the left of Priyanshu. If Priyanshu is 18th from the left end of the row, how far is Nirupaman from the right end of the row, what is the position of Nirupaman from the right end of the row? (SI 14 Jul 2023)
- 137
- 235
- 334
- 436
Show answer
Answer: 1 — 37
Priyanshu is 18th from the left end. Nirupaman is 6 places to Priyanshu's left, so Nirupaman stands at 18 − 6 = 12th from the left end. Now convert to the right end: position from the right = total − position from the left + 1 = 48 − 12 + 1 = 37. Option 4 (36) is what you get by writing 48 − 12 and forgetting the +1.
10 soldiers are standing in a straight line. There is twice the number of soldiers standing in front of Nishal as behind him. The number of soldiers standing in front of Gulshan is equal to the number of soldiers standing behind Nishal. How many soldiers are standing behind Gulshan? (SI 15 Jul 2023)
- 18
- 27
- 36
- 45
Show answer
Answer: 3 — 6
Leave Nishal out: 10 − 1 = 9 soldiers are either in front of him or behind him. In front = 2 × behind, so 2b + b = 9, b = 3 and in front = 6. Nishal therefore stands 7th from the front. Soldiers in front of Gulshan = soldiers behind Nishal = 3, so Gulshan stands 4th from the front. Behind Gulshan = 10 − 4 = 6. Picking 7 comes from counting Nishal's own position instead of the count behind Gulshan.
30 people are sitting in a row facing north. Roma is 15th from the right end of the row. If Aman sits 5th to the right of Roma, what is Aman's position from the right end of the row? (SI 31 Jul 2023)
- 18th
- 210th
- 39th
- 411th
Show answer
Answer: 2 — 10th
Roma is 15th from the right. Moving 5 places to the right takes Aman 5 places closer to the right end, so his position from the right end is 15 − 5 = 10th. The row's total of 30 is not needed at all, because both positions are counted from the same end. Option 3 (9th) comes from subtracting 5 and then adjusting by one, an off-by-one that the 'both counted from the same end' check rules out.
In a row of 42 primary class students facing the North for a photograph, Nayana is 4th to the left of Pranita. If Pranita is 20th from the left end of the row, then what is the position of Nayana from the right end of the row? (SI 31 Jul 2023)
- 127
- 225
- 326
- 424
Show answer
Answer: 1 — 27
Pranita is 20th from the left. Nayana stands 4 places to her left, so Nayana is 20 − 4 = 16th from the left end. In a row of n, position from the right = n − (position from the left) + 1. Here 42 − 16 + 1 = 27. Option 3 (26) is the classic off-by-one from forgetting the '+1' in that conversion.
All 40 students in a class are standing in a straight line facing north. Deepa is 15th from the right end while Karthik is 20th from the left end. How many students stand between Deepa and Karthik? (SI 31 Jul 2023)
- 16
- 25
- 38
- 47
Show answer
Answer: 2 — 5
Put both positions on the same end. Deepa is 15th from the right of 40, so from the left she is 40 − 15 + 1 = 26th. Karthik is 20th from the left. The number of students strictly between them is 26 − 20 − 1 = 5. Forgetting the final −1 gives 6 (option 1), which is the usual trap.
Identical arithmetic, printed with letters in place of names. Number the string from the left in pen and the rest is a lookup — the same habit that answers the nineteen position-and-rank questions in the series chapter.
All four, solved (4)Tap to open
Which of the following letters is fifth to the left of the ninth letter from the left end? (Left) V, O, N, P, T, A, D, E, B, J, Q, Z, X (Right) (SI 3 Jul 2023)
- 1D
- 2A
- 3P
- 4Z
Show answer
Answer: 3 — P
Number the arrangement from the left: 1 V, 2 O, 3 N, 4 P, 5 T, 6 A, 7 D, 8 E, 9 B, 10 J, 11 Q, 12 Z, 13 X. The ninth letter from the left is B at position 9. Fifth to the left of it is position 9 − 5 = 4, which holds P. Counting to the right instead gives Z, and stopping one short gives A or D — the three distractors.
Which letter is third to the right of the seventh letter from the left end? (Left) C, E, Z, K, M, O, J, T, X, A, U, G, H (Right) (SI 3 Jul 2023)
- 1K
- 2X
- 3U
- 4A
Show answer
Answer: 4 — A
Number from the left: 1 C, 2 E, 3 Z, 4 K, 5 M, 6 O, 7 J, 8 T, 9 X, 10 A, 11 U, 12 G, 13 H. The seventh letter from the left is J at position 7. Third to its right is position 7 + 3 = 10, which holds A. Counting only two places to the right gives X and counting four gives U — the two nearest distractors; K comes from counting to the left instead.
Which letter is midway between the ninth letter from the right and the third letter from the left? (Left) P, S, J, C, B, D, L, V, D, K, M, O, U, I, Z, W, E (Right). (SI 29 Jul 2023)
- 1D
- 2B
- 3S
- 4J
Show answer
Answer: 1 — D
Number the string from the left. There are 17 letters: 1 P, 2 S, 3 J, 4 C, 5 B, 6 D, 7 L, 8 V, 9 D, 10 K, 11 M, 12 O, 13 U, 14 I, 15 Z, 16 W, 17 E. Ninth from the right = position 17 − 9 + 1 = 9, which is D. Third from the left = position 3, which is J. Midway between positions 9 and 3 is position (9 + 3)/2 = 6, which is D. J (option 4) is one of the two endpoints, not the midpoint, and S and B are simply nearby letters.
In the given letter-cluster, which letter is third to the left of the eighth letter from the left end? (Left) F H M R O J V X B D N P (Right) (SI 31 Jul 2023)
- 1H
- 2V
- 3O
- 4B
Show answer
Answer: 3 — O
Number the string from the left: F(1) H(2) M(3) R(4) O(5) J(6) V(7) X(8) B(9) D(10) N(11) P(12). The eighth letter from the left is X at position 8. Third to the left of it is position 8 − 3 = 5, which is O. Option 2 (V) is only first to the left, the usual slip of counting from the wrong anchor.
Part 2 · Rank from both ends — 13 questions
Add the two ranks, then subtract one
When one person's rank is given from the top and from the bottom, the total is the two ranks added together minus one. The minus one is not a convention to memorise — it is there because that person has been counted in both numbers, and counting them once is enough. Note how different this is from the rule in Part 1. There, two different people's positions from opposite ends add to total + 1. Here, one person's two ranks add to total + 1 as well — so total = a + b − 1. The same arithmetic, read in the other direction, and the SI prints the off-by-one answer as an option every time.
“Narinder is 20th from the top” — he is rank 20; nineteen people are above him. “19 students rank above Narinder” — he is rank 20. The sentence counts the others, not him. “Narinder is 20th from the top and 15th from the bottom” — the class has 20 + 15 − 1 = 34 students. Translate every sentence into a rank number before doing anything with it.
Every other both-ends question (12)Tap to open
Shivani ranked 12th in a class of 59 students. What is her rank from the last? (SI 20 Jun 2023)
- 146
- 247
- 348
- 449
Show answer
Answer: 3 — 48
Use the standard rule: rank from top + rank from bottom = total + 1. Here the total is 59 and the rank from the top is 12, so the rank from the last = 59 − 12 + 1 = 48. Option 2 (47) is the classic off-by-one error, from doing 59 − 12 and forgetting to add the 1 that counts Shivani herself.
In a class of 68 students, 19 students obtained a rank higher than Narinder. Find the number of students who obtained a rank lower than Narendra. (SI 21 Jun 2023)
- 149
- 246
- 347
- 448
Show answer
Answer: 4 — 48
If 19 students rank above Narinder, then Narinder himself is 20th from the top. The students ranked below him are all the rest of the class: 68 − 20 = 48. Equivalently, total = (students above) + Narinder + (students below), so 68 = 19 + 1 + 48. Option 1, 49, is the trap: it is 68 − 19 and forgets to exclude Narinder himself.
During the oath-taking ceremony, the newly elected members are standing in a line. Smriti Gupta is 21st in order from both ends. How many members are there in the line? (SI 29 Jun 2023)
- 145
- 247
- 341
- 443
Show answer
Answer: 3 — 41
When one person's position is given from both ends, total = (position from left) + (position from right) − 1, because that person is counted twice. Total = 21 + 21 − 1 = 41. Option 4 (43) is what you get by adding 21 + 21 + 1, and option 1 (45) by forgetting the correction and adding a further pair.
Dev is 20th from the left end and 21st from the right end in the line of students in the school. How many students should be added in the row, so that there are 50 students in line? (SI 29 Jun 2023)
- 110
- 28
- 311
- 49
Show answer
Answer: 1 — 10
When one person's positions from both ends are given, total = (position from left) + (position from right) − 1, because that person is counted twice. Total now = 20 + 21 − 1 = 40. Students to be added = 50 − 40 = 10. Forgetting to subtract the 1 gives 41 and hence 9, which is the trap in option 4.
P, Q, R, S and T are selected for a university admission interview, according to the marks they have obtained in the entrance test. R has the least chance and T has the highest chance of getting the admission. The test was out of 140 marks, which included 50 marks for multiple choice questions, 30 for short answer questions, and 60 for long answer questions. P got full marks for the multiple choice questions and short answer questions, but lost half of the total for the long answer questions. Q got 3/5 of what P got. S got more than R, who got 6% less than Q's marks. S scored 128.04 marks. If the ranking of a candidate depends upon the merit list according to the marks they received in the test, who came third? (SI 9 Jul 2023)
- 1P
- 2Q
- 3T
- 4S
Show answer
Answer: 1 — P
Compute each score. P takes full marks in MCQ (50) and short answer (30) and loses half of the 60 long-answer marks, so P = 50 + 30 + 30 = 110. Q = (3/5) × 110 = 66. R = 6% less than Q = 66 − 3.96 = 62.04, which fits R having the least chance. S = 128.04, which is more than R as stated. T has the highest chance, so T > 128.04. The merit order from the top is therefore T (highest), S (128.04), P (110), Q (66), R (62.04). The third name on that list is P. The tempting wrong pick is S, who has the highest computed score among P, Q, R, S — but T outranks S, which pushes S to second and P to third.
Shivani ranked 12th in a class of 59 students. What is her rank from the last? (SI 14 Jul 2023)
- 149
- 247
- 346
- 448
Show answer
Answer: 4 — 48
Use the standard rank rule: rank from one end + rank from the other end = total + 1. So rank from the last = total − rank from the top + 1 = 59 − 12 + 1 = 48. Option 2 (47) is the classic slip of writing 59 − 12 and forgetting the +1 for Shivani herself.
In a poem recitation competition, Amyra ranked 4th from the top and her friend Syma ranked 5th from the bottom. Nihal ranked exactly in-between Amyra and Syma. If there were 4 students ranked between Amyra and Nihal, how many students were there in all? (SI 15 Jul 2023)
- 113
- 217
- 318
- 412
Show answer
Answer: 3 — 18
Nihal is exactly midway, so the 4 students between Amyra and Nihal are matched by 4 between Nihal and Syma. Build the line from the top: 3 students above Amyra (she is 4th), Amyra, 4 students, Nihal, 4 students, Syma, then 4 students below her (she is 5th from the bottom). Total = 3 + 1 + 4 + 1 + 4 + 1 + 4 = 18. 17 is what you get by forgetting to count Nihal himself.
Sita secured the 6th position from the top and the 10th position from the bottom in her class. How many students are there in the class? (SI 15 Jul 2023)
- 114
- 216
- 317
- 415
Show answer
Answer: 4 — 15
Rule: when one person's rank is counted from both ends, total = (rank from top) + (rank from bottom) − 1, because that person is counted twice. Total = 6 + 10 − 1 = 15. The usual slip is to add without subtracting, which gives 16 — option 2. Answer: option 4 (15).
Vivek is 37th from the right end and 27th from the left end of a line of school students. How many students should be added to the row so that there are 70 students in the line? (SI 15 Jul 2023)
- 143
- 233
- 363
- 47
Show answer
Answer: 4 — 7
When one person's position is counted from both ends, that person is counted twice, so total = (position from left) + (position from right) − 1 = 27 + 37 − 1 = 63 students at present. To reach 70 students, 70 − 63 = 7 more students must be added. 63 is the trap for anyone who answers with the present strength instead of the number to be added, and 33 comes from forgetting to subtract 1.
Vinay is 37th from both ends of a line of class 10 students. How many students must be removed from the line so that only 50 students remain in it? (SI 29 Jul 2023)
- 173
- 210
- 347
- 423
Show answer
Answer: 4 — 23
When a person's position is counted from both ends, the total is (position from one end) + (position from the other end) − 1, because that person is counted twice. So the line has 37 + 37 − 1 = 73 students. To leave only 50, remove 73 − 50 = 23 students. Option 1 (73) is the size of the line itself, not the number to be removed, and is the usual trap.
Sita ranked 6th from the top and 10th from the bottom in her class. How many students are there in the class? (SI 29 Jul 2023)
- 116
- 214
- 317
- 415
Show answer
Answer: 4 — 15
Total = rank from the top + rank from the bottom − 1, the −1 removing the double count of Sita herself. So the class has 6 + 10 − 1 = 15 students. Option 1 (16) is the classic slip of adding 6 and 10 without subtracting the one overlap.
In a row of people all facing north, Tina is 7th from the right end. Manju is 16th from the right end. Manju is exactly between Deepak and Tina. If Deepak is 10th from the left end of the row, then how many people in total are there in the row? (SI 31 Jul 2023)
- 134
- 235
- 336
- 433
Show answer
Answer: 1 — 34
Count everything from the right end. Tina is 7th from the right, Manju is 16th from the right, so the gap between them is 16 − 7 = 9 places. Manju is exactly midway between Deepak and Tina, so Deepak lies the same 9 places further left: Deepak is 16 + 9 = 25th from the right end. Deepak is also 10th from the left end, and his position is counted in both directions, so total = 25 + 10 − 1 = 34. The tempting slip is to add 25 + 10 = 35 (option 2) and forget that Deepak's own place is counted twice.
Part 3 · Comparison and ordering — 28 questions
Build one chain, and read the word “only” carefully
You are given five or six people and a handful of comparisons in sentences. The work is to turn each sentence into an inequality and then join them into a single chain, tallest on the left. Two habits make this reliable. First, use one symbol throughout — pick > and let it mean taller, or older, or higher-scoring, but never swap mid-question. Second, write the chain as you go rather than holding it in your head; a clue that does not yet connect goes on its own line until something links it. You will often find that the chain does not fully determine the order — two people may never be compared with each other. That is not a flaw in the question. Read what is actually asked: usually it is who is tallest, who is shortest, or who sits at one named place, and those are fixed even when the middle is not.
Every other chain-building question (11)Tap to open
The question below consists of a question and two statements numbered I and II given below it. You have to decide whether the data provided in the statements are sufficient to answer the question. Read both the statements and give answer : Who among Rakesh, Mukesh, Amit, Nitin and Sumit is the lightest? I- Amit is heavier than Mukesh and Sumit but lighter than Nitin. II- Nitin is not heaviest. (SI 16 Oct 2022)
- 1If the data in statement I alone are sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question
- 2If the data in statement II alone are sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question
- 3If the data given in both statements, statement I alone and statement II alone are independently sufficient to answer the question
- 4If the data given in both statements I and II together are not sufficient to answer the question
Show answer
Answer: 4 — If the data given in both statements I and II together are not sufficient to answer the question
From I: Nitin > Amit > Mukesh and Nitin > Amit > Sumit. Mukesh and Sumit are not compared with each other, and Rakesh is not placed at all, so the lightest could be Mukesh, Sumit or Rakesh — I alone is not sufficient. II alone gives only 'Nitin is not the heaviest' and says nothing about the bottom of the order — not sufficient. Combining: since Nitin is not heaviest and Nitin beats Amit, Mukesh and Sumit, the only person who can be above him is Rakesh. The order is Rakesh > Nitin > Amit > (Mukesh, Sumit). Mukesh and Sumit are still tied in ignorance, so the lightest is still not decided. Hence even both statements together are not sufficient.
Karan and Deepak are younger than Varun. Karan is older in age than Deepak and Krishna. Harish and Jatin are older than Krishna. Krishna is not the youngest. Who is the youngest? (SI 20 Jun 2023)
- 1Jatin
- 2Karan
- 3Krishna
- 4Deepak
Show answer
Answer: 4 — Deepak
Collect the comparisons, writing > for 'older than'. - Varun > Karan and Varun > Deepak. - Karan > Deepak and Karan > Krishna. - Harish > Krishna and Jatin > Krishna. Everyone named is older than Krishna except Deepak, whose position relative to Krishna is not given directly. The extra condition says Krishna is not the youngest, so somebody must sit below Krishna — and the only person left who can is Deepak. Option 3 (Krishna) is the trap: Krishna loses every comparison that mentions him, so he looks like the youngest until the last sentence rules it out.
A, B, C, D, E and F scored different marks. A scored more marks than E. E scored more marks than D. F is the person who scored between A and E. B scored the highest marks and D did not score the lowest marks. Who scored the lowest marks? (SI 20 Jun 2023)
- 1E
- 2C
- 3F
- 4A
Show answer
Answer: 2 — C
Build the order from the highest score downwards. - A > E and E > D give A > E > D. - F scored between A and E, so A > F > E, making the chain A > F > E > D. - B scored the highest, so B > A > F > E > D. That places five of the six, with C still unplaced. Since D did not score the lowest, someone must be below D, and C is the only person left. So the full order is B > A > F > E > D > C and C scored the lowest. Option 1 (E) and option 3 (F) are traps for anyone who stops before using the 'D is not the lowest' clue and forgets that C has to fit somewhere.
Sagar, Madhuri, Tia, Rita, Zain and Neha are six friends. Rita is shorter than Madhuri but taller than Zain. Sagar is the tallest. Tia is shorter than Madhuri but taller than Rita. Neha is the shortest. How many people are taller than Tia? (SI 2 Jul 2023)
- 12
- 21
- 33
- 44
Show answer
Answer: 1 — 2
Build one chain, tallest to shortest. - Sagar is the tallest, Neha the shortest. - Madhuri > Tia > Rita > Zain (Tia is below Madhuri but above Rita; Rita is above Zain). So the full order is Sagar > Madhuri > Tia > Rita > Zain > Neha. Only Sagar and Madhuri stand above Tia, i.e. 2 people. Option 2 ("1") is the trap for anyone who counts only Sagar and forgets that Madhuri is also above Tia.
There are six friends P, Q, R, S, T and U, each of a different age. Q is not the youngest of all. S and R are older than P and Q. T is older than Q and P. U is older than T but younger than S. Who is the youngest of all? (SI 2 Jul 2023)
- 1T
- 2Q
- 3P
- 4U
Show answer
Answer: 3 — P
Collect who is above whom. - S and R are both older than P and Q. - T is older than Q and P. - U is older than T, and S is older than U. So P and Q sit below S, R, T and U — the youngest must be P or Q. The first clause rules Q out explicitly ("Q is not the youngest"), so the youngest is P. T and U are both stated to be older than someone, so neither can be the bottom; that disposes of options 1 and 4.
There are six friends — Mridula, Durgesh, Gauri, Varun, Rajat and Anaya — each of a different age. Mridula is older than Durgesh but younger than Rajat. Anaya is older than Gauri but younger than Mridula. Varun is the youngest of all. Who is the oldest of all? (SI 14 Jul 2023)
- 1Anaya
- 2Gauri
- 3Mridula
- 4Rajat
Show answer
Answer: 4 — Rajat
Write each statement as an inequality with > meaning 'older than'. 'Mridula is older than Durgesh but younger than Rajat' gives Rajat > Mridula > Durgesh. 'Anaya is older than Gauri but younger than Mridula' gives Mridula > Anaya > Gauri. Joining the two chains: Rajat > Mridula > Anaya > Gauri, with Durgesh somewhere below Mridula, and Varun at the very bottom. Nobody is stated to be older than Rajat, so Rajat is the oldest. Mridula (option 3) is the tempting answer because she appears in both statements, but she is explicitly said to be younger than Rajat.
A, B, C, D, E, and F are standing together in a ground. D’s height is greater than that of B and F. F’s height is greater than that of B, A, and C. E is the tallest of the six. Who is the second tallest among these six? (SI 14 Jul 2023)
- 1D
- 2F
- 3A
- 4B
Show answer
Answer: 1 — D
Chain the statements. D > B and D > F. F > B, F > A, F > C. E is the tallest of all six. Since D is taller than F, and F is taller than A, B and C, D stands above five-sixths of the group; only E is above D. So the order from the top is E > D > F > (A, B, C in some order). The second tallest is D. F (option 2) is the trap because F beats three people by name, but D beats F directly. The relative heights of A, B and C are never fixed, and they do not need to be.
A, B, C, E, F and G are six friends who scored different marks in an examination. E scored less than B but more than A. F scored more than B but less than G. G scored less than C. A scored the lowest. How many persons scored less than B? (SI 15 Jul 2023)
- 12
- 24
- 31
- 43
Show answer
Answer: 1 — 2
Write each clue as an inequality and join them. A < E < B (E is below B, above A) B < F < G G < C A is lowest, which the chain already respects. Combined: A < E < B < F < G < C. Below B there are exactly two names, A and E. Answer: option 1 (2).
J, K, L, M, N and O are of different heights. O is shorter than N but not the shortest among all. L is taller than M but shorter than K. Only four persons are taller than O. N is shorter than M. Who is the tallest among all? (SI 31 Jul 2023)
- 1K
- 2O
- 3N
- 4M
Show answer
Answer: 1 — K
Chain the comparisons: K > L > M (from 'L taller than M but shorter than K'), then M > N ('N is shorter than M') and N > O ('O is shorter than N'). That gives K > L > M > N > O. 'Only four persons are taller than O' fixes O at the 5th place from the top — the four above him are exactly K, L, M and N — so the sixth person J must be below O, which also satisfies 'O is not the shortest'. Final order, tallest first: K > L > M > N > O > J. The tallest is K. Option 4 (M) is the trap for anyone who stops after linking M to N and O and never joins that chain to K.
A and B are younger than F. B and D are younger than A. E is the oldest. F is older than C. C is not the youngest. How many of these are younger than F? (SI 31 Jul 2023)
- 1Four
- 2Two
- 3Three
- 4Five
Show answer
Answer: 1 — Four
Write the clues as inequalities: F > A, F > B, A > B, A > D, F > C, and E is the oldest of all six, so E > F. Everyone except E is therefore below F. That leaves A, B, C and D younger than F — four people. 'C is not the youngest' only fixes C above B or D; it does not move anybody above F. Option 4 (Five) would need E below F, which contradicts E being the oldest.
A, B, C, D, E and F are 6 students who appeared for a Mathematics exam. C and D got exactly the same marks. F got the highest marks in the class. A and C got the least marks. B and E’s marks was the median of the whole data. Who got more marks than D? (SI 31 Jul 2023)
- 1A, E and F
- 2D, E and F
- 3B, E and F
- 4C, E and F
Show answer
Answer: 3 — B, E and F
Line the clues up. A and C are jointly lowest, and C = D, so A = C = D all sit at the bottom. B and E share the median, so they sit above the bottom group. F is highest of all. The order is A = C = D < B = E < F. Anyone above D is therefore B, E and F. Option 4 (C, E and F) fails because C equals D and so does not beat it; option 2 lists D itself.
10 of the 28 turn on one small word. “Only two friends are taller than O” is not a vague remark — it fixes O at place 3 from the top exactly, because it says there are two above and, by implication, everybody else below. “O is taller than only two” puts O at place 3 from the bottom. Same word, opposite ends. Whenever you see “only”, count how many people the sentence places on that side, add one, and you have the rank from that end. Then number the whole order and stop reasoning.
Every other “only” question (9)Tap to open
Six girls A, G, T, V, S and Q are different rank holders of a school. Only two girls have a rank higher than V. Only three girls have a rank between S and Q. Only T has a rank between Q's rank and A's rank. G's rank is immediately above S's rank. Who among all of them has got the highest rank? (SI 21 Jun 2023)
- 1A
- 2S
- 3V
- 4G
Show answer
Answer: 4 — G
Number the ranks 1 (highest) to 6 (lowest). Only two girls rank higher than V, so V is at rank 3. Exactly three girls lie between S and Q, so the gap between their ranks is 4. The only possible placements are (S, Q) at (1, 5), (2, 6), (5, 1) or (6, 2). G is immediately above S, so G = S − 1; that rules out S at rank 1. Try S = 5, G = 4, Q = 1: then A and T must fill ranks 2 and 6, but 'only T between Q and A' needs A two places from Q, i.e. rank 3, which V holds. Rejected. Try S = 6, G = 5, Q = 2: then A and T fill ranks 1 and 4; A would have to be at rank 4 with the in-between rank 3 held by V, not T. Rejected. Try Q = 6, S = 2, G = 1: A and T fill ranks 4 and 5. A must be two places from Q, so A = 4 and the girl between them, at rank 5, is T. This works. Final order: 1 G, 2 S, 3 V, 4 A, 5 T, 6 Q. ```puzzle:grid Rank 1: G Rank 2: S Rank 3: V Rank 4: A Rank 5: T Rank 6: Q ``` Check: two girls (G, S) above V; three girls (V, A, T) between S and Q; only T between Q and A; G immediately above S. S (option 2) is the trap because G and S sit together at the top and it is easy to read the pair the wrong way round.
Six friends named Khushi, Anushka, Pihu, Tanvi, Devanshi and Shrutu are talking about a quiz in which all of them took part. Shrutu scored more marks than Anushka and Tanvi. Devanshi scored less marks than only Khushi. Pihu scored more marks than Shrutu. Who scored the third highest marks? (Note that no two friends scored the same marks.) (SI 21 Jun 2023)
- 1Devanshi
- 2Shrutu
- 3Tanvi
- 4Pihu
Show answer
Answer: 4 — Pihu
Take the clues in order. 'Devanshi scored less than only Khushi' fixes the top two: Khushi first, Devanshi second. 'Pihu scored more than Shrutu' and 'Shrutu scored more than Anushka and Tanvi' chain together to put Pihu above Shrutu, and Shrutu above both Anushka and Tanvi. So the order runs Khushi > Devanshi > Pihu > Shrutu > (Anushka and Tanvi in some order), and third place is Pihu. Anushka and Tanvi cannot be separated from the clues given, but the question does not need them to be.
G, H, I, J, K and L scored different marks. Only four persons scored less than G. J scored less than I but did not score the lowest marks. H scored less than G but more than I. L scored the maximum marks among all. Who scored the lowest marks among all? (SI 3 Jul 2023)
- 1J
- 2K
- 3H
- 4G
Show answer
Answer: 2 — K
Six people, so 'only four scored less than G' puts G second from the top. L scored the most, so L > G. H < G but H > I, and J < I. That gives L > G > H > I > J, five people fixed in order. The only name left is K, and the only place left is the bottom. This also honours 'J did not score the lowest'. Full order (highest first): L, G, H, I, J, K. J is the tempting answer because J is low, but J is explicitly not the lowest.
K, L, M, N, O and P are of different ages. M is older than L but younger than P. Only three persons are younger than P. O is older than P but is not the oldest. L is older than N. Who is the oldest? (SI 9 Jul 2023)
- 1K
- 2P
- 3L
- 4M
Show answer
Answer: 1 — K
Order the six from youngest (1) to oldest (6). 'Only three persons are younger than P' puts P at position 4. The chain N < L < M (from 'M is older than L' and 'L is older than N') together with M < P fills positions 1, 2, 3 as N, L, M. O is older than P, so O is at 5 or 6, but O is not the oldest, so O is at 5. The only name left, K, takes position 6 and is the oldest. The tempting wrong pick is P, who is older than three people but still has O and K above him.
The test result of D, E, F, G, H and I is declared. Each of them scored different marks. G scored better than E and I only. F scored better than D and H. Who among the following scored the maximum? (SI 14 Jul 2023)
- 1I
- 2G
- 3H
- 4F
Show answer
Answer: 4 — F
The key word is 'only'. G scored better than E and I and nobody else, so exactly two people are below G and exactly three are above G — those three can only be D, F and H. That puts G fourth from the top. Among D, F and H, we are told F scored better than both D and H. So F is above the other two, and everyone else (G, E, I) is already below all three. The order is F > (D and H in some order) > G > (E and I in some order). F scored the maximum. Option 2 (G) is the trap for anyone who reads 'G scored better than E and I only' as G being at the top of the pair-comparisons.
L, M, N, O, P and Q are of different ages. L is older than Q but not the oldest among all. Only three persons are younger than Q. N is older than O but younger than P. Only three persons are older than P. Who is the oldest among all? (SI 15 Jul 2023)
- 1Q
- 2P
- 3M
- 4N
Show answer
Answer: 3 — M
Number the six from 1 (oldest) to 6 (youngest). - 'Only three persons are younger than Q' → Q has rank 3. - 'Only three persons are older than P' → P has rank 4. - N is older than O but younger than P → with 5 and 6 the only seats left below P, N = 5 and O = 6. - L is older than Q (rank 3) so L is rank 1 or 2, but L is not the oldest → L = 2. - The only name left for rank 1 is M. Final order: M > L > Q > P > N > O. P is the trap because it is named in a clue about people older than it, but that very clue pins it at rank 4.
In a group of friends named Rohan, Cherry, Mohan, Sohan, Pia and Aniya, each is of a different age. Rohan is older than only two of his friends. Piya is older than only five of her friends. If Aniya is younger than only Pia, then how many friends are younger than Aniya? Note that no two of them are of the same age. (SI 15 Jul 2023)
- 14
- 22
- 33
- 45
Show answer
Answer: 1 — 4
There are six friends, so 'older than only five friends' means older than everybody: Pia is the oldest, rank 1. 'Aniya is younger than only Pia' puts Aniya immediately below her, rank 2. With Aniya second of six, the four names below her — Rohan and three others — are younger. (Rohan, older than exactly two, sits fourth, which is consistent.) Order: Pia > Aniya > _ > Rohan > _ > _. Answer: option 1 (4).
In a group of 6 kids R, S, T, U, V and W, each one is of a different age. T is younger than U, who is older than W, who is older than V and R only. If S is older than U, who is the oldest among all of them? (SI 31 Jul 2023)
- 1U
- 2W
- 3S
- 4T
Show answer
Answer: 3 — S
'W is older than V and R only' fixes W above just those two and below everyone else, so W is fourth. T is younger than U, and U is above W, so the order from oldest is U > T > W > (V and R in some order). S is older than U, and no clue places anybody above S. Order: S > U > T > W > V/R. U is the trap — U beats T and W, but S is explicitly above U.
M, N, O, P, Q and R are students of class 9th who scored different marks in final exam. M scored less than O. Only N scored between M and O. Q scored less than R and more than O. P scored the minimum. How many students scored more than O? (SI 31 Jul 2023)
- 12
- 21
- 33
- 44
Show answer
Answer: 1 — 2
Take ascending marks. M < O with only N in between gives M < N < O. Q is more than O and less than R, so O < Q < R. P is the minimum, so P sits below M. The full order is P < M < N < O < Q < R. Above O there are exactly two students, Q and R. Option 3 tempts if you also count N, but N is below O.
A few questions give relations with numbers in them — Q is six years older than P, M is four years older than Q — or multiples, L is twice P and N is a quarter of L. Do not try to order these by reasoning. Give the smallest quantity a letter or the value 1, work out every other value from it, and then sort the numbers. Arithmetic is faster and cannot be misremembered halfway down a chain.
All six, solved (6)Tap to open
A, B, C, D, E and F are of different ages. B is two years younger than F and 20 years older than C. C is five years older than D. E is two years younger than B. A is 3 years older than F. D's age is the square root of A's age, which is 36. After 2 years, A goes to another country and F and C take care of D. After another 2 years, C has to go to another country and F has to take care of D. B comes to help F. After three years, B travels, so E comes to help F. After one year, F travels, so E and D live together. How old was E when he came to help D? (SI 1 Jul 2023)
- 130
- 234
- 336
- 437
Show answer
Answer: 3 — 36
Step 1 — fix the present ages. The stem states A = 36 (and D = sqrt(36) = 6). - A = F + 3 → F = 33 - B = F − 2 → B = 31 - B = C + 20 → C = 11 (consistent with C = D + 5 = 11 ✓) - E = B − 2 → E = 29 Step 2 — walk the timeline. Elapsed · Event +2 · A leaves; F and C look after D +2 more (year 4) · C leaves; F looks after D; B comes to help +3 more (year 7) · B travels; E comes to help +1 more (year 8) · F travels; E and D live together E arrives in year 7, so E's age then = 29 + 7 = 36. The trap is option 1 (30): that is E's age one year after the start, i.e. using the wrong event on the timeline.
There are six persons M, N, O, P, Q and R, and each of them is of a different age. M is 4 years older than Q, who is 6 years older than P. M is 2 years younger than R but 8 years older than N. O is younger than Q and P. Who is the oldest among all six friends? (SI 1 Jul 2023)
- 1R
- 2N
- 3M
- 4Q
Show answer
Answer: 1 — R
Take P's age as x and build up. - Q = P + 6 = x + 6 - M = Q + 4 = x + 10 - R = M + 2 = x + 12 - N = M − 8 = x + 2 - O < P and O < Q, so O < x Order, oldest first: R (x+12) > M (x+10) > Q (x+6) > N (x+2) > P (x) > O. M (option 3) is the trap — M is older than everyone the question names explicitly except R, and R appears only in the clause "M is 2 years younger than R".
A, B, C, D, E and F are of different ages. B is two years younger than F and 20 years older than C. C is five years older than D. E is two years younger than B. A is 3 years older than F. D's age is the square root of A's age, which is 36. After 2 years, A goes to another country and F and C take care of D. After another 2 years, C has to go to another country and F has to take care of D. B comes to help F. After three years, B travels, so E comes to help F. After one year, F travels, so E and D live together. Show, as an inequality, the relationship between the ages of A, B and C after 7 years. (SI 2 Jul 2023)
- 1A > B > C
- 2A < B > C
- 3A < B < C
- 4A > B < C
Show answer
Answer: 1 — A > B > C
A = 36, so D = sqrt(36) = 6. Then C = D + 5 = 11, B = C + 20 = 31, F = B + 2 = 33 and A = F + 3 = 36 — the chain closes on the same 36, so the reading is right. (E = B − 2 = 29.) Person · A · B · C · D · E · F Age now · 36 · 31 · 11 · 6 · 29 · 33 Everyone ages by the same 7 years, so the order never changes: A = 43, B = 38, C = 18, i.e. A > B > C. Option 2 and option 4 both need C to beat B, but B was set 20 years above C, and option 3 reverses the whole chain. The travel story changes only who lives with whom, not any age.
L, M, N, O, P and Q are cousins having different ages. The age of L is two times of P and that of Q is four times that of P. Age of N is one-fourth of L. Age of O is one and half times of M and age of M is three times that of L. Who among them is at the 3rd position in order of age from highest to lowest? (SI 15 Jul 2023)
- 1M
- 2P
- 3O
- 4Q
Show answer
Answer: 4 — Q
Take P = 1 and read every relation off it. - L = 2 × P = 2 - Q = 4 × P = 4 - N = L/4 = 0.5 - M = 3 × L = 6 - O = 1.5 × M = 9 Highest to lowest: O (9) > M (6) > Q (4) > L (2) > P (1) > N (0.5). The third name in that list is Q. The tempting wrong answer is M, which is only second — O beats it because O is one and a half times M.
A, B, C, D, E and F are six friends who scored different marks in an examination. 1. A scored two times more marks than C. 2. C scored four times more marks than E and two times more marks than F. 3. B was at the fifth position. 4. D scored the least marks. Who among them was at the third position? (SI 29 Jul 2023)
- 1A
- 2E
- 3C
- 4F
Show answer
Answer: 4 — F
Put C at 4 units. Then A = 2C = 8, F = C/2 = 2 and E = C/4 = 1. That fixes A > C > F > E. D has the least marks, so D is sixth, and B is given as fifth. The full order from the top is A (8), C (4), F (2), E (1), B, D, so the third position belongs to F. Option 3 (C) is the trap for anyone who forgets that B and D are slotted in at the bottom and counts C as third from the wrong end.
P, Q, R, S, T and U are selected for a university admission interview, according to the marks they have obtained in the entrance test. The test was out of 140 marks which included 40 marks for multiple-choice questions, 40 for short answer questions, and 60 for long answer questions. R got full marks for the multiple-choice questions and half marks for the short answer questions and got 30% of what P got in the long answer questions. T and U scored 50% of the total marks of the short answer and multiple-choice questions. S scored 10 marks more than T and U in the short answer and multiple-choice questions. T, U and S each scored 50 marks in the long answer questions. P scored 10% more than U in the long answer questions and a total of 60 in the short answer and multiple-choice questions. Q scored 20 less than P. Who got the lowest score? (SI 31 Jul 2023)
- 1T
- 2R
- 3U
- 4S
Show answer
Answer: 2 — R
Work out each total. Multiple-choice + short answer is 40 + 40 = 80 marks; long answer is 60. R: full 40 in MCQ and half of 40 = 20 in short answer, so 60 in the two together. T and U: 50% of 80 = 40 each in the two together; S: 40 + 10 = 50. T, U, S each got 50 in the long answer. P got 60 in MCQ + short answer, and 10% more than U in the long answer = 50 + 10% of 50 = 55. So P = 60 + 55 = 115. Q = P - 20 = 95. R's long answer = 30% of P's long answer = 30% of 55 = 16.5, so R = 60 + 16.5 = 76.5. Candidate · MCQ + short answer · Long answer · Total P · 60 · 55 · 115 Q · - · - · 95 R · 60 · 16.5 · 76.5 S · 50 · 50 · 100 T · 40 · 50 · 90 U · 40 · 50 · 90 The lowest total is R's 76.5. T and U (90 each) are the trap — they look weak on the objective part, but R loses far more on the 60-mark long answer section.
Part 4 · The exam-hall routine
Four lines on the rough sheet
- Pick one direction
- Convert the ends
- Number the places
- Re-read the question
- Subtracting a left position from a right position. They run in opposite directions. Convert with n + 1 − p first.
- Forgetting the −1 for a person counted twice. Rank 8 from the top and 5 from the bottom means 12 people, not 13.
- Confusing “between” with “from”. People between places 7 and 15 number 7; places from one to the other number 8. Both are printed.
- Reading “only three are younger” as “he is third”. It makes him fourth from the youngest. Count the people named, then add one.
- Swapping the meaning of > halfway through. Decide once that > means taller, and write every clue that way even when the sentence says “shorter than”.
- From left + from right = total + 1.
- One person, both ends: total = a + b − 1.
- “Only k above X” → X is (k + 1)th from the top.
- “X above only k” → X is (k + 1)th from the bottom.
- Between places a and b: b − a − 1 people.
- Facing north, right is east; facing south, west.
- Numbers in the clues → set the smallest to 1 and compute.
- One symbol throughout. Never flip > mid-question.
- An incomplete chain still answers “who is tallest”.
- Always re-read the question after building the order.