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Paper IPaper I · General Mental Ability

General Mental Ability, Full Practice Set (50 Questions)

Fifty authored mixed quantitative aptitude and reasoning questions with a full answer key and worked explanations

CAPF wiki•8 min read•16 sections
At a glance
PaperPaper ISubjectGMASyllabusGeneral Mental Ability: logical reasoning, quantitative aptitude including numerical ability, and data interpretationImportanceHigh
GMAPractice SetQuantitative AptitudeReasoningMixedPaper 1

A mixed 50-question drill across the whole module: number system, percentages and ratios, profit and interest, time-speed-work, mensuration, permutation-combination and probability, clocks and calendars, data sufficiency, and reasoning. All questions are authored for this wiki and are not verbatim previous-year questions. The arithmetic in every answer has been checked.

Suggested method: time yourself at about 45 to 50 seconds per question to mimic exam pace, then mark against the key. For the marking and guessing logic, see exam strategy and shortcuts.

Section A: Number system and simplification (Q1 to Q8)

  1. Simplify: 36 + 12 of 2 minus 48 / 8 + 5.
  2. Find the HCF of 48 and 60.
  3. Find the LCM of 9, 12, and 15.
  4. Find the unit digit of 3 to the power 24.
  5. Is 73,584 (that is 73584) divisible by 8?
  6. Find the sum 1 + 2 + 3 + ... + 40.
  7. Simplify: (5 to the power 6 times 5 to the power 2) / 5 to the power 5.
  8. The HCF of two numbers is 6 and their LCM is 180. One number is 36. Find the other.

Section B: Percentage, ratio, average, profit and interest (Q9 to Q18)

  1. What is 35 percent of 240?
  2. A number increased by 20 percent becomes 144. Find the number.
  3. Divide an allotment of 480 in the ratio 3 : 5.
  4. The average of five numbers is 18. If a sixth number 30 is added, find the new average.
  5. A shopkeeper buys an item for 800 rupees and sells it for 920 rupees. Find the profit percent.
  6. An article marked at 600 rupees is sold at a 15 percent discount. Find the selling price.
  7. Find the simple interest on 5,000 rupees at 8 percent per annum for 3 years.
  8. Find the compound interest on 10,000 rupees at 10 percent per annum for 2 years.
  9. The ratio of two numbers is 4 : 7 and their sum is 88. Find the larger number.
  10. A man spends 75 percent of his income and saves 2,500 rupees a month. Find his monthly income.

Section C: Time, speed, distance, and work (Q19 to Q26)

  1. Convert 108 km/h to m/s.
  2. A 180 m train crosses a pole in 12 seconds. Find its speed in km/h.
  3. A car covers 240 km in 4 hours. Find its average speed.
  4. A boat's still-water speed is 12 km/h and the stream is 3 km/h. Find the downstream and upstream speeds.
  5. A and B do a job in 12 days and 24 days respectively. How long working together?
  6. A pipe fills a tank in 5 hours; a leak empties it in 10 hours. With both open, how long to fill?
  7. Two trains 150 m and 100 m long run towards each other at 50 km/h and 40 km/h. How long to cross?
  8. A man covers a distance at 30 km/h and returns at 45 km/h. Find the average speed for the whole trip.

Section D: Mensuration and geometry (Q27 to Q33)

  1. Find the area of a rectangle 18 m by 12 m.
  2. Find the circumference of a circle of radius 21 cm (π = 22/7).
  3. A right triangle has legs 8 cm and 15 cm. Find the hypotenuse.
  4. Find the volume of a cube of side 6 cm.
  5. Find the volume of a cylinder of radius 7 cm and height 5 cm (π = 22/7).
  6. Find the sum of interior angles of a regular pentagon.
  7. Find the area of a triangle with sides 5 cm, 12 cm, and 13 cm.

Section E: Permutation, combination and probability (Q34 to Q39)

  1. In how many ways can 6 books be arranged on a shelf?
  2. From 9 players, how many ways to choose a team of 3?
  3. How many distinct arrangements of the letters of the word ARROW?
  4. A die is rolled. Find the probability of getting a number greater than 4.
  5. A card is drawn from a pack of 52. Find the probability it is a red king.
  6. Two coins are tossed. Find the probability of getting at least one head.

Section F: Clocks and calendars (Q40 to Q43)

  1. Find the angle between the hands at 2:00.
  2. How many odd days are there in an ordinary year?
  3. If 1 January 2023 is a Sunday, what day is 1 January 2024? (2023 is an ordinary year.)
  4. Find the angle between the hands at 3:15.

Section G: Reasoning and data sufficiency (Q44 to Q50)

  1. In a row of 30 students, Anil is 12th from the left. What is his position from the right?
  2. Statements: All apples are fruits. All fruits are foods. Does "All apples are foods" follow?
  3. Find the next term: 2, 6, 12, 20, 30, ?
  4. If in a code MONDAY is written as NPOEBZ, how is FRIDAY written?
  5. Pointing to a man, a woman said, "His mother is the only daughter of my mother." How is the woman related to the man?
  6. Data sufficiency. Question: What is x? Statement I: 3x = 21. Statement II: x is odd. Which is sufficient (use codes A, B, C, D, E as in data sufficiency)?
  7. Find the odd one out: 8, 27, 64, 100, 125.

Answer key with explanations

Section A

Reveal the answer key and full worked solutions
  1. "of" first: 12 of 2 = 24. Then 36 + 24 minus 48/8 + 5 = 36 + 24 minus 6 + 5 = 59.
  2. 48 = 24 times 3; 60 = 22 times 3 times 5. Common = 22 times 3 = 12. HCF = 12.
  3. 9 = 32, 12 = 22 times 3, 15 = 3 times 5. LCM = 22 times 32 times 5 = 180.
  4. 3 cycles 3, 9, 7, 1 (length 4). 24 mod 4 = 0, which lands on the last in the cycle, 1. Unit digit is 1.
  5. Last three digits 584; 584 / 8 = 73 exactly, so yes, divisible by 8.
  6. n(n+1)/2 with n = 40: 40 times 41 / 2 = 820.
  7. 56+2 / 55 = 58 / 55 = 53 = 125.
  8. LCM times HCF = product, so 180 times 6 = 1080 = 36 times other; other = 1080/36 = 30.

Section B

Reveal the answer key and full worked solutions
  1. 35 percent of 240 = 0.35 times 240 = 84.
  2. 2 times number = 144, so number = 144 / 1.2 = 120.
  3. Total 480 in 3 : 5 (8 parts). One part = 60. Shares = 180 and 300.
  4. Old sum = 5 times 18 = 90. New sum = 90 + 30 = 120 over 6 numbers. New average = 120/6 = 20.
  5. Profit = 920 minus 800 = 120. Profit percent = 120/800 times 100 = 15 percent.
  6. Discount = 15 percent of 600 = 90. Selling price = 600 minus 90 = 510 rupees.
  7. SI = P times R times T / 100 = 5000 times 8 times 3 / 100 = 1200 rupees.
  8. Amount = 10000 times (1.1)2 = 10000 times 1.21 = 12100. CI = 12100 minus 10000 = 2100 rupees.
  9. Total parts 4 + 7 = 11; one part = 88/11 = 8. Larger = 7 times 8 = 56.
  10. Savings 25 percent of income = 2500, so income = 2500 / 0.25 = 10,000 rupees.

Section C

Reveal the answer key and full worked solutions
  1. 108 times 5/18 = 30 m/s.
  2. Speed = 180/12 = 15 m/s = 15 times 18/5 = 54 km/h.
  3. 240 / 4 = 60 km/h.
  4. Downstream = 12 + 3 = 15 km/h; upstream = 12 minus 3 = 9 km/h.
  5. LCM(12, 24) = 24 units. A does 24/12 = 2/day, B does 24/24 = 1/day, together 3/day. Time = 24/3 = 8 days.
  6. Tank = LCM(5, 10) = 10 units. Fill = 10/5 = 2/h, leak = 10/10 = 1/h (negative). Net = 1/h. Time = 10 hours.
  7. Relative speed = 50 + 40 = 90 km/h = 25 m/s. Distance = 150 + 100 = 250 m. Time = 250/25 = 10 seconds.
  8. Average for equal distances = 2ab/(a+b) = 2 times 30 times 45 / 75 = 2700/75 = 36 km/h.

Section D

Reveal the answer key and full worked solutions
  1. 18 times 12 = 216 square m.
  2. 2 times (22/7) times 21 = 2 times 22 times 3 = 132 cm.
  3. (8, 15, 17) triple. Hypotenuse = √(64 + 225) = √(289) = 17 cm.
  4. 63 = 216 cubic cm.
  5. π times r2 times h = (22/7) times 49 times 5 = 22 times 7 times 5 = 770 cubic cm.
  6. (5 minus 2) times 180 = 3 times 180 = 540°.
  7. (5, 12, 13) is a right triangle, so area = (1/2) times 5 times 12 = 30 square cm.

Section E

Reveal the answer key and full worked solutions
  1. 6! = 720.
  2. 9C3 = (9 times 8 times 7)/(3 times 2 times 1) = 504/6 = 84.
  3. ARROW has 5 letters with R twice: 5!/2! = 120/2 = 60.
  4. Numbers greater than 4 are 5 and 6: 2/6 = 1/3.
  5. Red kings = 2 (hearts and diamonds): 2/52 = 1/26.
  6. P(at least one head) = 1 minus P(no head) = 1 minus 1/4 = 3/4.

Section F

Reveal the answer key and full worked solutions
  1. abs(30 times 2 minus 5.5 times 0) = abs(60) = 60°.
  2. 365 mod 7 = 1 odd day.
  3. 2023 is ordinary, 1 odd day. Sunday plus 1 = Monday.
  4. abs(30 times 3 minus 5.5 times 15) = abs(90 minus 82.5) = 7.5°.

Section G

Reveal the answer key and full worked solutions
  1. From right = 30 minus 12 + 1 = 19th.
  2. Yes; apples are inside fruits, which are inside foods, so all apples are foods.
  3. Differences are 4, 6, 8, 10, so the next difference is 12: 30 + 12 = 42. (Equivalently the terms are n(n+1): 1 times 2, 2 times 3, ...; the 6th is 6 times 7 = 42.)
  4. Each letter shifts forward by 1: M to N, O to P, and so on. FRIDAY becomes GSJEBZ (F to G, R to S, I to J, D to E, A to B, Y to Z).
  5. "The only daughter of my mother" is the woman herself, so the man's mother is the woman; she is his mother.
  6. Code A. Statement I gives x = 7 (unique). Statement II allows many odd numbers, so not sufficient alone.
  7. 100 is the odd one out; 8 = 23, 27 = 33, 64 = 43, 125 = 53 are perfect cubes, but 100 = 102 is a perfect square, not a cube.

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