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UCAT · Practice Sheet 36

Sheet code: UCAT-S36 · 20 questions

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

    The marked price of an item is £1,400. After a 40% 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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  2. 2.
    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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  3. 3.
    Quantitative Aptitude

    The marked price of an item is £700. After a 15% 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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  4. 4.
    Quantitative Aptitude

    A value changes from 900 to 450. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  5. 5.
    Quantitative Aptitude

    Find the HCF and LCM of 21 and 30.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  6. 6.
    Quantitative Aptitude

    A invests £5,000 and B invests £7,000 for the same period. If the total profit is £13,000, find A's share.

    Formula:Partnership (profit share)
    ShareA=Profit×AA+B\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}
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  7. 7.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  8. 8.
    Quantitative Aptitude

    Find the simple interest on £40,000 at 4% per annum for 6 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  9. 9.
    Quantitative Aptitude

    A value changes from 200 to 100. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  10. 10.
    Quantitative Aptitude

    Find the compound interest on £18,000 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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  11. 11.
    Quantitative Aptitude

    A vehicle covers 158 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  12. 12.
    Quantitative Aptitude

    Find the average of these 5 numbers: 49, 37, 76, 55, 31.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  13. 13.
    Quantitative Aptitude

    Find the HCF and LCM of 28 and 27.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  14. 14.
    Quantitative Aptitude

    Pipe A fills a tank in 14 hours and pipe B in 15 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

    A can finish a job in 19 days and B in 15 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  16. 16.
    Quantitative Aptitude

    What is 50% of 720?

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

    Find the HCF and LCM of 26 and 38.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  18. 18.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 5?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  19. 19.
    Quantitative Aptitude

    The sum of the ages of two people is 90 years, and one is 10 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  20. 20.
    Quantitative Aptitude

    Find the average of these 10 numbers: 60, 68, 65, 28, 72, 47, 58, 87, 68, 48.

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