| Section | Questions | Topics | Marks |
|---|---|---|---|
| Quantitative Ability | 50 | Arithmetic, Algebra, Geometry, Mensuration, Ratios, Percentages, Work/Time | 50 |
| Logical Reasoning & DI | 50 | Syllogisms, Puzzles, Directions, Blood Relations, Charts/Tables | 50 |
| English / Verbal Ability | 50 | Reading Comprehension, Vocabulary, Grammar, Verbal Reasoning | 50 |
| Total | 150 | PYQ-based High-Difficulty Questions | 150 |
Q1–10: Advanced Arithmetic / Number Sense
Q1. A sum of money doubles in 5 years at simple interest. In how many years will it triple at the same rate?
A. 7.5 years
B. 10 years
C. 12.5 years
D. 15 years
Q2. Two numbers are in the ratio 7:11. If their product is 5390, the numbers are:
A. 35, 55
B. 49, 77
C. 70, 110
D. 77, 121
Q3. A shopkeeper sells an article at 25% profit. If he had bought it at 20% less, his profit would have been 50%. Cost price = ?
A. ₹160
B. ₹200
C. ₹240
D. ₹250
Q4. If x−12+x+23=1, find x.
A. 2
B. 3
C. 4
D. 5
Q5. A person invests ₹10000 at compound interest 10% per annum compounded annually. Amount after 2 years = ?
A. ₹12100
B. ₹12000
C. ₹11000
D. ₹11550
Q6. The difference between the squares of two numbers is 99. If their sum = 11, the numbers are:
A. 5, 6
B. 7, 4
C. 9, 2
D. 8, 3
Q7. A train passes a pole in 18 seconds and a platform 120 m long in 30 seconds. Length of train = 60 m. Speed?
A. 12 m/s
B. 10 m/s
C. 15 m/s
D. 20 m/s
Q8. A sum at compound interest doubles in 4 years. In how many years will it become 8 times?
A. 8
B. 12
C. 16
D. 14
Q9. If (x−3)(x+5)=14, x = ?
A. 4
B. 3
C. 6
D. -2
Q10. A bag contains 5 red, 7 blue, 8 green balls. Two balls drawn at random. Probability both are green?
A. 14/190
B. 28/190
C. 7/38
D. 4/19
Q11–20: Advanced Algebra / Percentages
Q11. Solve: x2–7x+10=0
A. 5, 2
B. 1, 10
C. 2, 5
D. 3, 4
Q12. A number is increased by 25% and then decreased by 20%. Net change = ?
A. +5%
B. 0%
C. +2%
D. -5%
Q13. Sum of three numbers is 120. The first is twice the second, the third is 5 more than the first. Find numbers.
A. 40, 20, 60
B. 50, 25, 45
C. 60, 30, 65
D. 30, 15, 65
Q14. The average of 7 numbers is 32. One number = 50. Average of remaining?
A. 30
B. 31
C. 32
D. 33
Q15. A number is divided into two parts such that 4 times the first plus 5 times the second = 100. If the sum = 25, the first number = ?
A. 15
B. 10
C. 12
D. 8
Q16. The price of a shirt is marked 25% above cost. After a discount of 20%, the shopkeeper’s profit % = ?
A. 0%
B. 5%
C. 3%
D. 4%
Q17. A sum of ₹7200 is divided among A, B, C such that A:B = 2:3, B:C = 4:5. A’s share = ?
A. ₹1200
B. ₹1600
C. ₹1800
D. ₹2000
Q18. The simple interest on a sum for 3 years at 12% per annum = ₹432. Principal?
A. ₹1200
B. ₹1000
C. ₹1500
D. ₹1100
Q19. If a number is decreased by 15% and then increased by 20%, net % change = ?
A. +2%
B. +5%
C. -2%
D. -3%
Q20. A and B can do a job in 12 and 16 days respectively. Both work together. Fraction of work done in 1 day?
A. 7/48
B. 5/24
C. 3/16
D. 1/8
Q21–30: Advanced Geometry / Mensuration
Q21. Area of a triangle with sides 13, 14, 15 = ? (Use Heron’s formula)
A. 84
B. 90
C. 78
D. 80
Q22. Two concentric circles have radii 14 cm and 7 cm. Area of ring? (π=22/7)
A. 462 cm²
B. 308 cm²
C. 154 cm²
D. 210 cm²
Q23. Volume of cone with radius 7 cm, height 24 cm (π=22/7)
A. 1232 cm³
B. 1540 cm³
C. 1848 cm³
D. 1230 cm³
Q24. Cylinder radius 7 cm, height 15 cm. Volume? (π=22/7)
A. 2310 cm³
B. 2205 cm³
C. 2450 cm³
D. 2500 cm³
Q25. Perimeter of triangle with sides 13, 14, 15 = ?
A. 42
B. 40
C. 43
D. 45
Q26. A cuboid has volume 864 cm³. Length = 12, breadth = 8. Height = ?
A. 9 cm
B. 8 cm
C. 12 cm
D. 6 cm
Q27. Diagonal of cube = 10√3 cm. Side = ?
A. 10
B. 8
C. 12
D. 9
Q28. Area of trapezium with bases 10, 14 and height 6 = ?
A. 72
B. 60
C. 80
D. 84
Q29. Surface area of sphere radius 7 cm? (π=22/7)
A. 616 cm²
B. 554 cm²
C. 462 cm²
D. 498 cm²
Q30. Volume of sphere radius 7 cm? (π=22/7)
A. 1436 cm³
B. 1540 cm³
C. 1232 cm³
D. 1000 cm³
Q31–40: Data Interpretation / Ratios / Work & Time
Q31. The ratio of boys to girls in a school is 7:5. If there are 840 boys, total students = ?
A. 1200
B. 1500
C. 1400
D. 1600
Q32. A bag contains 8 red, 7 blue, and 5 green balls. Two balls are drawn without replacement. Probability that both are blue = ?
A. 7/95
B. 7/38
C. 7/30
D. 7/60
Q33. Average marks of 8 students = 75. If two new students scored 80 and 90, new average = ?
A. 78
B. 76.5
C. 77.5
D. 79
Q34. x:y = 5:7 and x + y = 96. Find y.
A. 56
B. 60
C. 64
D. 48
Q35. A sum of ₹9000 is divided among A, B, C such that A:B:C = 2:3:4. Find C’s share.
A. ₹4000
B. ₹3600
C. ₹4500
D. ₹5000
Q36. A, B, C can do a job in 12, 15, 20 days respectively. If they work together, fraction of work done in 1 day = ?
A. 1/5
B. 3/20
C. 1/6
D. 7/60
Q37. Pipe A can fill a tank in 20 hours, pipe B in 30 hours. Both open together, time to fill tank = ?
A. 12 hours
B. 10 hours
C. 15 hours
D. 25 hours
Q38. Two numbers are in ratio 9:16. If their HCF = 5, numbers are:
A. 45, 80
B. 40, 75
C. 35, 64
D. 30, 50
Q39. A sum of money is lent at compound interest 8% per annum. If it amounts to ₹17496 in 2 years, principal = ?
A. ₹15000
B. ₹16000
C. ₹14000
D. ₹14500
Q40. A and B start a business with investments in ratio 5:3. Profit after 1 year = ₹6400. A’s share = ?
A. ₹4000
B. ₹3000
C. ₹3500
D. ₹3600
Q41–50: Advanced Word Problems / High-Difficulty
Q41. A cistern can be filled by pipe A in 12 hours and emptied by pipe B in 16 hours. If both are open together, tank fills in:
A. 48/7 hours
B. 24/5 hours
C. 12/5 hours
D. 16/7 hours
Q42. A sum of money triples in 5 years at compound interest. Annual rate?
A. 25.99%
B. 24%
C. 26%
D. 27%
Q43. Two trains start from the same point at same time, one at 60 km/h and another at 80 km/h. How far apart after 3 hours?
A. 60 km
B. 66 km
C. 70 km
D. 75 km
Q44. The ratio of ages of A and B is 5:7. After 5 years, ratio = 6:8. Find B’s present age.
A. 35
B. 28
C. 30
D. 32
Q45. A sum at CI amounts to ₹1320 in 2 years and ₹1452 in 3 years. Rate of interest?
A. 10%
B. 12%
C. 15%
D. 8%
Q46. A box contains 6 red, 5 green, 4 blue balls. Two balls drawn randomly. Probability of different colors = ?
A. 67/91
B. 65/91
C. 70/91
D. 60/91
Q47. A sum at SI of ₹3000 at 5% for n years yields interest ₹750. n = ?
A. 5
B. 4
C. 6
D. 3
Q48. A train covers a distance in 5 hours at speed x km/h. If speed is increased by 10 km/h, time reduced by 30 minutes. Find x.
A. 60
B. 50
C. 40
D. 45
Q49. The sum of squares of two numbers = 290. One number = 7. Other = ?
A. 17
B. 13
C. 15
D. 11
Q50. A can do a job in 8 days, B in 12 days. They start together. After 4 days, A leaves. Remaining work done by B alone. Total days to finish work = ?
A. 8
B. 9
C. 10
D. 7
Q51–60: Logical Reasoning – Statements & Assumptions
Q51. Statement: “All roses are flowers. Some flowers fade quickly.”
Which conclusion follows?
A. All roses fade quickly
B. Some roses may fade quickly
C. No rose fades quickly
D. All flowers are roses
Q52. Statement: “If it rains, the match will be postponed. The match was not postponed.”
Conclusion?
A. It rained
B. It did not rain
C. Match was cancelled
D. No conclusion
Q53. Statement: “All students who study hard succeed. Ravi studies hard.”
Conclusion?
A. Ravi will succeed
B. Ravi may fail
C. Ravi is lucky
D. No conclusion
Q54. Statement: “Some birds are black. All black objects absorb heat.”
Conclusion?
A. Some birds absorb heat
B. All birds absorb heat
C. All black objects are birds
D. No conclusion
Q55. Statement: “Only fruits have seeds. Mango has seeds.”
Conclusion?
A. Mango is fruit
B. Mango may not be fruit
C. Mango is vegetable
D. No conclusion
Q56. Statement: “No mobile phone is cheap. Some cheap items are toys.”
Conclusion?
A. Some toys are not mobile phones
B. All toys are expensive
C. Some cheap items are mobile phones
D. No conclusion
Q57. Statement: “All managers are employees. Some employees are punctual.”
Conclusion?
A. Some managers are punctual
B. All managers are punctual
C. No manager is punctual
D. Cannot be determined
Q58. Statement: “If a student scores above 90, he gets a scholarship. Anand got a scholarship.”
Conclusion?
A. Anand scored above 90
B. Anand may have scored below 90
C. Anand is intelligent
D. No conclusion
Q59. Statement: “Some cars are electric. All electric devices consume less energy.”
Conclusion?
A. Some cars consume less energy
B. All cars consume less energy
C. Some cars do not consume less energy
D. No conclusion
Q60. Statement: “Every law requires approval from parliament. This law is approved.”
Conclusion?
A. This is a law
B. This may not be a law
C. Parliament approved a law
D. Cannot conclude
Q61–70: Logical Deduction / Syllogism
Q61. Statements: “All dogs are animals. Some animals are pets.”
Conclusion?
A. Some dogs are pets
B. All pets are dogs
C. Some animals may not be dogs
D. No dogs are pets
Q62. Statements: “All cats are mammals. No mammal can fly.”
Conclusion?
A. All cats cannot fly
B. Some cats can fly
C. All mammals can fly
D. Cannot conclude
Q63. Statements: “All pencils are writing instruments. Some writing instruments are pens.”
Conclusion?
A. Some pencils may be pens
B. No pencil is pen
C. Some pens are pencils
D. Cannot conclude
Q64. Statements: “No student is lazy. All lazy people fail exams.”
Conclusion?
A. Some students fail exams
B. No student fails exam
C. Some students may fail
D. Cannot conclude
Q65. Statements: “All books are informative. Some books are novels.”
Conclusion?
A. Some novels are informative
B. All novels are informative
C. No novels are informative
D. Cannot conclude
Q66. Statements: “Some fruits are sour. All lemons are sour.”
Conclusion?
A. Some fruits are lemons
B. All sour things are lemons
C. Some lemons are fruits
D. Cannot conclude
Q67. Statements: “No computer is slow. Some devices are slow.”
Conclusion?
A. No computer is a device
B. Some devices are not computers
C. All devices are computers
D. Cannot conclude
Q68. Statements: “All students in class A passed. Some students in class B passed.”
Conclusion?
A. Some students passed in both classes
B. All students passed in B
C. Cannot conclude
D. No student passed in B
Q69. Statements: “Some actors are singers. All singers are talented.”
Conclusion?
A. Some actors are talented
B. All actors are talented
C. No actor is talented
D. Cannot conclude
Q70. Statements: “All birds have wings. Penguins are birds.”
Conclusion?
A. Penguins have wings
B. Penguins can fly
C. Penguins are not birds
D. Cannot conclude
Q71–80: Analytical Reasoning / Blood Relations & Directions
Q71. Pointing to a man, Rahul says: “He is the son of my mother’s only brother.” The man is Rahul’s:
A. Cousin
B. Nephew
C. Uncle
D. Brother
Q72. A is 10 m east of B. C is 15 m north of B. Distance between A and C?
A. 18 m
B. 15 m
C. 17 m
D. 20 m
Q73. If A + B means A is father of B, A × B means A is mother of B, A – B means A is brother of B. If P + Q × R, Q is ?
A. Father
B. Mother
C. Sister
D. Cannot tell
Q74. A is south of B. C is west of B. D is north of C. Which direction is D from A?
A. Northwest
B. Northeast
C. Southwest
D. Southeast
Q75. P is brother of Q. R is son of Q. S is daughter of P. How is R related to S?
A. Cousin
B. Brother
C. Uncle
D. Nephew
Q76. If in a family, A’s mother is B, B’s mother is C, C’s father is D. How is D related to A?
A. Grandfather
B. Father
C. Great-grandfather
D. Uncle
Q77. A starts from P, walks 5 km north, then 3 km east. Distance from starting point = ?
A. 4 km
B. √34 km
C. √25 km
D. 8 km
Q78. If “some pens are pencils, all pencils are erasers”, which is true?
A. Some pens are erasers
B. All pens are erasers
C. No pen is eraser
D. Cannot conclude
Q79. A family has 3 generations: 4 males, 3 females. Statements: John is father of Lisa, Lisa’s daughter is Mary, etc. How many females?
A. 3
B. 2
C. 4
D. 1
Q80. Five friends sit in a row. P left of Q, R right of S, T at extreme left. Who is in the middle?
A. Q
B. P
C. R
D. S
Q81–90: Data Sufficiency / Logical Puzzles
Q81. Is x > y?
(1) x – y = 5
(2) x + y = 15
A. Statement 1 alone sufficient
B. Statement 2 alone sufficient
C. Both needed
D. Not sufficient
Q82. Find the number of students who play cricket:
(1) 60% play cricket
(2) Total students = 50
A. Statement 1 alone
B. Statement 2 alone
C. Both needed
D. Not sufficient
Q83. A box has red, blue, green balls. Find probability of green ball:
(1) Total balls = 30
(2) 10 green balls
A. Statement 1 alone
B. Statement 2 alone
C. Both needed
D. Either statement enough
Q84. Five people P, Q, R, S, T sit in a row. Who sits leftmost?
(1) T sits extreme right
(2) P sits left of Q
A. 1 alone
B. 2 alone
C. Both needed
D. Cannot tell
Q85. A number is divisible by 3?
(1) Sum of digits = 18
(2) Number is even
A. 1 alone
B. 2 alone
C. Both needed
D. Not sufficient
Q86. A cube is painted on all sides. How many small cubes with 2 painted faces?
(1) Cube divided into 27 small cubes
(2) Only 1 face removed
A. 1 alone
B. 2 alone
C. Both needed
D. Cannot tell
Q87. A train travels from A to B at 60 km/h. Time = 5 h. Distance?
(1) Average speed = 60 km/h
(2) Journey time = 5 h
A. 1 alone
B. 2 alone
C. Both needed
D. Either statement enough
Q88. Find x: 3x + 2y = 16, x – y = 2
A. Cannot solve
B. x = 4
C. x = 3
D. x = 5
Q89. A bag contains red and blue balls. Probability of red = 1/2. How many balls?
(1) Total = 10
(2) Red = 5
A. 1 alone
B. 2 alone
C. Both needed
D. Either sufficient
Q90. A sum at 10% SI for 2 years = ₹220. Principal?
(1) Rate = 10%
(2) Time = 2 years
A. 1 alone
B. 2 alone
C. Both needed
D. Either sufficient
Q91–100: Advanced Data Interpretation / Logic & Charts
Q91. A company’s revenue (₹ lakh) over 5 years: 2018 – 120, 2019 – 150, 2020 – 180, 2021 – 210, 2022 – 240.
Find the average revenue over 5 years.
A. 180
B. 200
C. 190
D. 210
Q92. In a class of 60 students, 30 study Maths, 25 study Science, 10 study both. Number of students who study either Maths or Science = ?
A. 45
B. 40
C. 50
D. 55
Q93. Sales (units) of 3 products over 4 quarters:
- Product A: 50, 60, 70, 80
- Product B: 40, 50, 60, 70
- Product C: 30, 40, 50, 60
Total sales of Product B over 4 quarters = ?
A. 200
B. 220
C. 210
D. 230
Q94. A pie chart shows expenditure: Rent – 30%, Food – 25%, Transport – 15%, Others – 30%. Total = ₹60,000. How much spent on Food?
A. ₹15,000
B. ₹12,000
C. ₹18,000
D. ₹14,000
Q95. A survey: 120 students, favourite sport – Football 40, Cricket 50, Hockey 30. Probability randomly chosen student likes Hockey = ?
A. 1/4
B. 1/3
C. 1/2
D. 1/5
Q96. A logic puzzle: P, Q, R, S, T live on 5 different floors (1–5).
- P above Q
- R below S
- T on 5th floor
Who is on 3rd floor?
A. P
B. Q
C. R
D. S
Q97. A company’s profit in 6 months: Jan – 12, Feb – 15, Mar – 18, Apr – 16, May – 20, Jun – 19 lakh.
Average profit = ?
A. 16 lakh
B. 16.5 lakh
C. 17 lakh
D. 17.5 lakh
Q98. Table shows students passing in subjects:
- Maths – 30, Science – 25, Both – 10
Number of students passing only one subject = ?
A. 35
B. 30
C. 25
D. 40
Q99. Five friends: A, B, C, D, E run races. D finishes before B but after C. E finishes last. Who is second?
A. B
B. D
C. C
D. A
Q100. A bar graph shows production of 4 factories: F1 – 120, F2 – 150, F3 – 180, F4 – 200 units.
Factory contributing 25% of total production = ?
A. F1
B. F2
C. F3
D. F4
Disclaimer:
This sample paper is created for educational and practice purposes only. The questions are inspired by previous year trends to help students prepare. It is not an official exam paper and does not guarantee exact representation of the actual IPM/NPAT or any other test. Users are advised to use it solely for learning, practice, and self-assessment.
| Q.No | Answer |
|---|---|
| 51 | B |
| 52 | B |
| 53 | A |
| 54 | A |
| 55 | A |
| 56 | A |
| 57 | D |
| 58 | A |
| 59 | A |
| 60 | A |
| 61 | C |
| 62 | A |
| 63 | D |
| 64 | B |
| 65 | A |
| 66 | C |
| 67 | B |
| 68 | C |
| 69 | A |
| 70 | A |
| 71 | A |
| 72 | C |
| 73 | B |
| 74 | A |
| 75 | A |
| 76 | C |
| 77 | B |
| 78 | D |
| 79 | A |
| 80 | B |
| 81 | C |
| 82 | C |
| 83 | B |
| 84 | C |
| 85 | A |
| 86 | A |
| 87 | D |
| 88 | B |
| 89 | C |
| 90 | C |
| 91 | A |
| 92 | C |
| 93 | C |
| 94 | B |
| 95 | B |
| 96 | A |
| 97 | C |
| 98 | A |
| 99 | C |
| 100 | B |