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UCAT · Practice Sheet 30

Sheet code: UCAT-S30 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    Quantitative Aptitude

    Find the compound interest on £17,000 at 20% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  2. 2.
    Quantitative Aptitude

    The marked price of an item is £1,500. After a 5% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
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  3. 3.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  4. 4.
    Quantitative Aptitude

    Find the average of these 8 numbers: 49, 63, 57, 38, 46, 56, 25, 54.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  5. 5.
    Quantitative Aptitude

    The marked price of an item is £1,600. After a 50% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  6. 6.
    Quantitative Aptitude

    A vehicle covers 276 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  7. 7.
    Quantitative Aptitude

    Two varieties costing £38 and £85 per kg are mixed to give a mixture worth £65 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)
    q1q2=p2−mm−p1\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}
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  8. 8.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  9. 9.
    Quantitative Aptitude

    What is 10% of 400?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  10. 10.
    Quantitative Aptitude

    Find the average of these 10 numbers: 88, 28, 28, 78, 31, 38, 46, 63, 47, 60.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  11. 11.
    Quantitative Aptitude

    Find the compound interest on £14,000 at 10% per annum compounded annually for 3 years.

    Formula:Compound Interest
    A=P(1+R100)TA = P\left(1+\dfrac{R}{100}\right)^{T}
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  12. 12.
    Quantitative Aptitude

    Divide £3,250 between two people in the ratio 6:7. How much does each receive?

    Formula:Sharing in a Ratio
    Share=Total×partsum of parts\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}
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  13. 13.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 6?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  14. 14.
    Quantitative Aptitude

    Pipe A fills a tank in 7 hours and pipe B in 4 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
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  15. 15.
    Quantitative Aptitude

    An item is bought for £900 and sold for £1,080. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  16. 16.
    Quantitative Aptitude

    What is 75% of 480?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  17. 17.
    Quantitative Aptitude

    A vehicle covers 184 km in 4 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  18. 18.
    Quantitative Aptitude

    Find the HCF and LCM of 17 and 17.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  19. 19.
    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  20. 20.
    Quantitative Aptitude

    A can finish a job in 18 days and B in 4 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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