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UCAT · Practice Sheet 19

Sheet code: UCAT-S19 · 20 questions

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

    A vehicle covers 560 km in 7 hours. Find its average speed.

    Formula:Speed, Distance & Time
    Speed=DistanceTime\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}
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  2. 2.
    Quantitative Aptitude

    Two varieties costing £22 and £68 per kg are mixed to give a mixture worth £31 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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  3. 3.
    Quantitative Aptitude

    Find the average of these 8 numbers: 74, 63, 78, 36, 28, 82, 89, 37.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  4. 4.
    Quantitative Aptitude

    Divide £2,590 between two people in the ratio 6:4. 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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  5. 5.
    Quantitative Aptitude

    Find the average of these 5 numbers: 36, 58, 87, 22, 80.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  6. 6.
    Quantitative Aptitude

    Find the compound interest on £8,000 at 20% 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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  7. 7.
    Quantitative Aptitude

    Divide £1,573 between two people in the ratio 4:7. 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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  8. 8.
    Quantitative Aptitude

    A invests £2,000 and B invests £7,000 for the same period. If the total profit is £18,000, 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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  9. 9.
    Quantitative Aptitude

    Find the simple interest on £17,000 at 12% per annum for 5 year(s).

    Formula:Simple Interest
    SI=P×R×T100SI = \dfrac{P\times R\times T}{100}
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  10. 10.
    Quantitative Aptitude

    The sum of the ages of two people is 55 years, and one is 7 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  11. 11.
    Quantitative Aptitude

    Find the simple interest on £25,000 at 8% per annum for 5 year(s).

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

    Two varieties costing £11 and £78 per kg are mixed to give a mixture worth £38 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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  13. 13.
    Quantitative Aptitude

    A can finish a job in 18 days and B in 16 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
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  14. 14.
    Quantitative Aptitude

    Find the HCF and LCM of 10 and 23.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  15. 15.
    Quantitative Aptitude

    Pipe A fills a tank in 12 hours and pipe B in 13 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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  16. 16.
    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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  17. 17.
    Quantitative Aptitude

    A vehicle covers 210 km in 7 hours. Find its average speed.

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

    Find the HCF and LCM of 33 and 16.

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

    An item is bought for £400 and sold for £480. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  20. 20.
    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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