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CAT Practice Questions
Original practice questions for the Common Admission Test (Indian Institutes of Management (convening IIM rotates)), mixed across 7 topics with instant answers and explanations. Practise by topic below or take the timed mock test.
CAT mixed practice
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Q1.PercentagesTwo successive discounts of 10% and 12% are equivalent to a single discount of:
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Answer: C — 20.8%
Net discount = a + b − ab/100 = 10 + 12 − 10×12/100 = 20.8%.
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Q2.Ratio, Ages & MixturesThe present ages of two people are in the ratio 3:2. After 4 years the sum of their ages will be 63. What is the present age of the elder person?
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Answer: D — 33 years
Let ages be 3x and 2x. After 4 years: 3x + 4 + 2x + 4 = 63 → 5x = 55 → x = 11. Elder = 3×11 = 33 years.
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Q3.Time, Work & PipesPipe A fills a tank in 6 hours and pipe B empties it in 9 hours. If both are opened, the tank fills in:
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Answer: A — 18 hours
Net rate = 1/6 − 1/9 = 3/54 of the tank per hour → 54/3 = 18 hours.
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Q4.AlgebraFind the sum of the first 19 terms of the AP 4, 12, 20, …
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Answer: C — 1444
Sₙ = n/2 × [2a + (n − 1)d] = 19/2 × [8 + 144] = 1,444.
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Q5.Geometry & MensurationFind the distance between (4, 1) and (9, 13).
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Answer: B — 13
Distance = √((Δx)² + (Δy)²) = √(5² + 12²) = 13.
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Q6.Data InterpretationThe average of 9 numbers is 73. If 104 is added, what is the new average?
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Answer: D — 76.1
Old total = 9 × 73 = 657. New total = 657 + 104 = 761; new average = 761/10 = 76.1.
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Q7.Verbal Reasoning & AnalogiesStatement: “Use our toothpaste for whiter teeth.” Assumption I: People want whiter teeth. II: Other toothpastes do not whiten.
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Answer: A — Only I is implicit
The ad assumes people desire whiter teeth; it does not assume competitors fail.
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Q8.PercentagesWhat is 60% of 80?
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Answer: A — 48
60% of 80 = 60/100 × 80 = 48.
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Q9.Ratio, Ages & MixturesThe present ages of two people are in the ratio 3:2. After 5 years the sum of their ages will be 45. What is the present age of the elder person?
Show answer & explanation
Answer: B — 21 years
Let ages be 3x and 2x. After 5 years: 3x + 5 + 2x + 5 = 45 → 5x = 35 → x = 7. Elder = 3×7 = 21 years.
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Q10.AlgebraSolve: 3x + 4y = 65 and 2x + y = 25
Show answer & explanation
Answer: B — x = 7, y = 11
Elimination/substitution gives x = 7, y = 11. Check: 3(7) + 4(11) = 65 ✓ and 2(7) + 1(11) = 25 ✓.
About CAT
Common Admission Test — conducted by Indian Institutes of Management (convening IIM rotates). The entrance exam for IIM MBA programmes, with VARC, DILR and Quantitative Ability sections.
Original practice questions written for this site in the style and difficulty of each exam’s syllabus. They are not past papers and the site is not affiliated with any exam body. Exam patterns, marking schemes and syllabi change — always check the latest official notification.
Practise by topic
- Percentages questions — Convert percentages to fractions you know by heart (12.5% = 1/8, 37.5% = 3/8, 16.67% = 1/6) and always divide a change by the ORIGINAL value.
- Ratio, Ages & Mixtures questions — Write the ratio as parts (e.g.
- Time, Work & Pipes questions — Turn each rate into work per day (1/10 of the job per day) or use the LCM of the days as total work.
- Algebra questions — Factorise quadratics by finding two numbers with the right sum and product; check roots by substitution.
- Geometry & Mensuration questions — Memorise core formulas (circle πr², triangle ½bh, Pythagoras, distance √((x₂−x₁)² + (y₂−y₁)²)).
- Data Interpretation questions — Read the table title, units and years before calculating.
- Verbal Reasoning & Analogies questions — For syllogisms draw Venn diagrams and accept only what MUST be true.
- CAT mock test — 25 timed questions with negative marking.
CAT practice topics
| Topic | Section | Question source |
|---|---|---|
| Percentages | Quantitative aptitude | Calculated (new numbers every set) |
| Ratio, Ages & Mixtures | Quantitative aptitude | Calculated (new numbers every set) |
| Time, Work & Pipes | Quantitative aptitude | Calculated (new numbers every set) |
| Algebra | Mathematics | Calculated (new numbers every set) |
| Geometry & Mensuration | Mathematics | Calculated (new numbers every set) |
| Data Interpretation | Data interpretation | Calculated (new numbers every set) |
| Verbal Reasoning & Analogies | Reasoning | Calculated + question bank |