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UCAT · Practice Sheet 44

Sheet code: UCAT-S44 · 20 questions

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

    Two varieties costing £29 and £89 per kg are mixed to give a mixture worth £57 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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  2. 2.
    Quantitative Aptitude

    A invests £9,000 and B invests £6,000 for the same period. If the total profit is £38,000, 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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  3. 3.
    Quantitative Aptitude

    Pipe A fills a tank in 13 hours and pipe B in 5 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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  4. 4.
    Quantitative Aptitude

    Find the average of these 10 numbers: 26, 87, 83, 44, 89, 36, 57, 46, 70, 69.

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

    Two fair dice are rolled. What is the probability that the sum of the numbers is 7?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  6. 6.
    Quantitative Aptitude

    A vehicle covers 558 km in 9 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

    A value changes from 800 to 960. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  8. 8.
    Quantitative Aptitude

    A can finish a job in 10 days and B in 12 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  9. 9.
    Quantitative Aptitude

    What is 75% of 280?

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

    A value changes from 800 to 960. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  11. 11.
    Quantitative Aptitude

    Find the simple interest on £20,000 at 5% per annum for 6 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  12. 12.
    Quantitative Aptitude

    A invests £10,000 and B invests £5,000 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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  13. 13.
    Quantitative Aptitude

    Pipe A fills a tank in 12 hours and pipe B in 3 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  14. 14.
    Quantitative Aptitude

    A value changes from 400 to 420. Find the percentage increase.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
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  15. 15.
    Quantitative Aptitude

    The marked price of an item is £1,800. After a 30% 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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  16. 16.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 4?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  17. 17.
    Quantitative Aptitude

    Find the HCF and LCM of 17 and 26.

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

    What is 20% of 700?

    Formula:Percentage of a Number
    Value=P100×N\text{Value} = \dfrac{P}{100}\times N
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  19. 19.
    Quantitative Aptitude

    Find the HCF and LCM of 20 and 10.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  20. 20.
    Quantitative Aptitude

    A vehicle covers 405 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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