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CAT previous-year-style questions — the arithmetic-heavy Quantitative Ability, plus Logical Reasoning, Data Interpretation and Verbal Ability problems that decide your percentile. Original, exam-grade, with full solutions.

20 questions1 setUpdated 8 August 2026QA · DILR · VARC
ArithmeticAlgebraNumber SystemGeometryModern MathsLogical ReasoningVerbal Ability

August 2026

Latest
8 August 2026·20 questions·monthly

Fresh set — 20 CAT-level questions across QA, DILR and VARC.

  1. 1Arithmetic · Profit & LossHardNumerical
    A trader marks his goods 50% above cost and then offers two successive discounts of 20% and 10%. What is his profit percentage?
    Show answer & solution
    Correct answer
    8
    Solution

    Take CP = 100. MP = 150. SP = 150 × 0.80 × 0.90 = 108. Profit = 108 − 100 = 8%.

  2. 2Arithmetic · PercentageMediumNumerical
    If A’s salary is 25% more than B’s, then B’s salary is what percent less than A’s?
    Show answer & solution
    Correct answer
    20
    Solution

    Let B = 100, then A = 125. B is less than A by 25, so 25/125 × 100 = 20%.

  3. 3Arithmetic · Time-Speed-DistanceHardNumerical
    A car covers a route at 60 km/h and returns along the same route at 40 km/h. What is its average speed for the whole trip (in km/h)?
    Show answer & solution
    Correct answer
    48
    Solution

    For equal distances, average speed is the harmonic mean: 2×60×4060+40=4800100=48\dfrac{2 \times 60 \times 40}{60 + 40} = \dfrac{4800}{100} = 48 km/h.

  4. 4Arithmetic · Time & WorkHardNumerical
    A can finish a job in 12 days and B in 16 days. They work together for 4 days, then A leaves. How many more days does B need to finish the remaining work?
    Show answer & solution
    Correct answer
    20/3 ≈ 6.67
    Solution

    In 4 days together they do 4(112+116)=4×748=7124(\tfrac1{12}+\tfrac1{16}) = 4 \times \tfrac{7}{48} = \tfrac{7}{12}. Remaining = 5/12. B’s rate = 1/16, so time = (5/12) ÷ (1/16) = 80/12 = 20/3 ≈ 6.67 days.

  5. 5Arithmetic · MixturesMediumNumerical
    A 16-litre vessel contains milk and water in the ratio 5 : 3. How much water (in litres) must be added to make the ratio 1 : 1?
    Show answer & solution
    Correct answer
    4
    Solution

    Milk = 10 L, water = 6 L. For 1 : 1 the water must equal the milk (10 L), so add 10 − 6 = 4 L.

  6. 6Arithmetic · SI & CIMediumNumerical
    What is the difference between the compound interest and the simple interest on ₹8,000 for 2 years at 5% per annum (in ₹)?
    Show answer & solution
    Correct answer
    20
    Solution

    For 2 years the difference is P(r100)2=8000×(0.05)2=8000×0.0025=20P\left(\tfrac{r}{100}\right)^2 = 8000 \times (0.05)^2 = 8000 \times 0.0025 = 20.

  7. 7AlgebraHardNumerical
    If x+1x=3x + \dfrac{1}{x} = 3, find the value of x3+1x3x^3 + \dfrac{1}{x^3}.
    Show answer & solution
    Correct answer
    18
    Solution

    x3+1x3=(x+1x)3−3(x+1x)=27−9=18x^3 + \tfrac1{x^3} = \left(x+\tfrac1x\right)^3 - 3\left(x+\tfrac1x\right) = 27 - 9 = 18.

  8. 8Algebra · QuadraticsMediumNumerical
    What is the sum of the roots of 2x2−8x+6=02x^2 - 8x + 6 = 0?
    Show answer & solution
    Correct answer
    4
    Solution

    Sum of roots =−ba=82=4= -\dfrac{b}{a} = \dfrac{8}{2} = 4 (the roots are 1 and 3).

  9. 9Algebra · LogarithmsMediumNumerical
    Evaluate log⁡28+log⁡327\log_2 8 + \log_3 27.
    Show answer & solution
    Correct answer
    6
    Solution

    log⁡28=3\log_2 8 = 3 and log⁡327=3\log_3 27 = 3, so the sum is 6.

  10. 10Number SystemHardNumerical
    What is the remainder when 71007^{100} is divided by 5?
    Show answer & solution
    Correct answer
    1
    Solution

    7≡2(mod5)7 \equiv 2 \pmod 5, so we need 2100 mod 52^{100} \bmod 5. Since 24≡12^4 \equiv 1 and 100=4×25100 = 4 \times 25, 2100≡12^{100} \equiv 1.

  11. 11Number SystemHardNumerical
    How many trailing zeros does 25!25! have?
    Show answer & solution
    Correct answer
    6
    Solution

    Count factors of 5: ⌊25/5⌋+⌊25/25⌋=5+1=6\lfloor 25/5 \rfloor + \lfloor 25/25 \rfloor = 5 + 1 = 6 (factors of 2 are more plentiful).

  12. 12Arithmetic · AveragesMediumNumerical
    The average of 5 numbers is 20. When a 6th number is added, the average becomes 25. What is the 6th number?
    Show answer & solution
    Correct answer
    50
    Solution

    New total = 6 × 25 = 150; old total = 5 × 20 = 100. The 6th number = 150 − 100 = 50.

  13. 13GeometryHardNumerical
    Find the area of a triangle with sides 13, 14 and 15 (in square units).
    Show answer & solution
    Correct answer
    84
    Solution

    By Heron’s formula, s=21s = 21; area =21⋅8⋅7⋅6=7056=84= \sqrt{21 \cdot 8 \cdot 7 \cdot 6} = \sqrt{7056} = 84.

  14. 14GeometryMediumMCQ
    A circle is inscribed in a square of side 10. What is the ratio of the circle’s area to the square’s area?
    • A) π/2\pi/2
    • B) π/4\pi/4
    • C) π/3\pi/3
    • D) π\pi
    Show answer & solution
    Correct answer
    B
    Solution

    Circle radius = 5, area =25π= 25\pi; square area = 100. Ratio =25π/100=π/4≈0.785= 25\pi/100 = \pi/4 \approx 0.785.

  15. 15Modern Maths · P&CMediumNumerical
    How many distinct arrangements can be made of the letters of the word "LEVEL"?
    Show answer & solution
    Correct answer
    30
    Solution

    LEVEL has 5 letters with L twice and E twice: 5!2! 2!=1204=30\dfrac{5!}{2!\,2!} = \dfrac{120}{4} = 30.

  16. 16Modern Maths · ProbabilityHardNumerical
    Two fair dice are rolled. What is the probability that the sum is a prime number? (give the fraction)
    Show answer & solution
    Correct answer
    5/12
    Solution

    Prime sums are 2, 3, 5, 7, 11 with 1 + 2 + 4 + 6 + 2 = 15 outcomes. Probability = 15/36 = 5/12.

  17. 17Algebra · InequalitiesHardNumerical
    How many integer values of xx satisfy ∣x−3∣<5|x - 3| < 5?
    Show answer & solution
    Correct answer
    9
    Solution

    −5<x−3<5⇒−2<x<8-5 < x - 3 < 5 \Rightarrow -2 < x < 8. Integers −1, 0, …, 7 give 9 values.

  18. 18Logical ReasoningMediumMCQ
    Five friends P, Q, R, S, T sit in a row. Q is exactly in the middle. P is at one end. S is immediately to the right of Q. Which of the following must be true?
    • A) T is at an end
    • B) R is immediately left of Q
    • C) S is at an end
    • D) P is next to Q
    Show answer & solution
    Correct answer
    A
    Solution

    Q is 3rd (middle); S is 4th. P is at an end (1st or 5th) but 4th and 3rd are taken, and if P were 5th, S(4th) blocks—so P is 1st, leaving R at 2nd and T at 5th (an end). Thus T is at an end.

  19. 19Data InterpretationMediumNumerical
    In a pie chart of a monthly budget, the "Rent" sector spans 108°. What percentage of the budget is Rent?
    Show answer & solution
    Correct answer
    30
    Solution

    A full circle is 360°. 108360×100=30%\dfrac{108}{360} \times 100 = 30\%.

  20. 20Verbal AbilityMediumMCQ
    Choose the option that best completes the sentence: "The committee’s decision was met with ______ criticism, as almost no one agreed with it."
    • A) muted
    • B) widespread
    • C) reluctant
    • D) grudging
    Show answer & solution
    Correct answer
    B
    Solution

    "Almost no one agreed" signals broad opposition, so the criticism was widespread. "Muted" would contradict the clause.

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