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UCAT · Practice Sheet 29

Sheet code: UCAT-S29 · 20 questions

Name: ______________
Date: ______________
  1. 1.
    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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  2. 2.
    Quantitative Aptitude

    Divide £942 between two people in the ratio 2:4. 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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  3. 3.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)

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

    A can finish a job in 13 days and B in 18 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  5. 5.
    Quantitative Aptitude

    The marked price of an item is £300. 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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  6. 6.
    Quantitative Aptitude

    Find the simple interest on £12,000 at 5% per annum for 2 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  7. 7.
    Quantitative Aptitude

    Find the compound interest on £1,000 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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  8. 8.
    Quantitative Aptitude

    A can finish a job in 17 days and B in 6 days. Working together, how long will they take?

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

    Pipe A fills a tank in 7 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?

    Formula:Pipes & Cisterns
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  10. 10.
    Quantitative Aptitude

    In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
    View formula →
  11. 11.
    Quantitative Aptitude

    Find the compound interest on £6,000 at 10% per annum compounded annually for 2 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

    A invests £4,000 and B invests £2,000 for the same period. If the total profit is £15,000, 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

    A vehicle covers 305 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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  14. 14.
    Quantitative Aptitude

    A can finish a job in 10 days and B in 16 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  15. 15.
    Quantitative Aptitude

    The sum of the ages of two people is 58 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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  16. 16.
    Quantitative Aptitude

    The marked price of an item is £1,200. After a 5% discount, find the selling price.

    Formula:Discount & Selling Price
    SP=MP(1−d100)SP = MP\left(1-\dfrac{d}{100}\right)
    View formula →
  17. 17.
    Quantitative Aptitude

    In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)

    Formula:Combinations
    nCr=n!r! (n−r)!^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}
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  18. 18.
    Quantitative Aptitude

    Find the simple interest on £20,000 at 5% per annum for 1 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
    View formula →
  19. 19.
    Quantitative Aptitude

    Find the average of these 5 numbers: 80, 81, 42, 71, 90.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  20. 20.
    Quantitative Aptitude

    Pipe A fills a tank in 15 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?

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

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