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UCAT · Practice Sheet 9

Sheet code: UCAT-S09 · 20 questions

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

    In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)

    Formula:Permutations
    nPr=n!(n−r)!^{n}P_{r} = \dfrac{n!}{(n-r)!}
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  2. 2.
    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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  3. 3.
    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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  4. 4.
    Quantitative Aptitude

    An item is bought for £200 and sold for £300. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
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  5. 5.
    Quantitative Aptitude

    The sum of the ages of two people is 65 years, and one is 15 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  6. 6.
    Quantitative Aptitude

    Two fair dice are rolled. What is the probability that the sum of the numbers is 8?

    Formula:Probability (two dice)
    P=favourabletotalP = \dfrac{\text{favourable}}{\text{total}}
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  7. 7.
    Quantitative Aptitude

    The sum of the ages of two people is 73 years, and one is 15 years older than the other. Find their ages.

    Formula:Ages (linear equations)
    x+(x+d)=Sx + (x+d) = S
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  8. 8.
    Quantitative Aptitude

    Divide £1,100 between two people in the ratio 2:2. 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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  9. 9.
    Quantitative Aptitude

    An item is bought for £800 and sold for £880. Find the profit percentage.

    Formula:Profit Percentage
    Profit%=SP−CPCP×100\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100
    View formula →
  10. 10.
    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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  11. 11.
    Quantitative Aptitude

    Find the compound interest on £14,000 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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  12. 12.
    Quantitative Aptitude

    A value changes from 500 to 400. Find the percentage decrease.

    Formula:Percentage Change
    % change=∣new−old∣old×100\%\,\text{change} = \dfrac{|new-old|}{old}\times 100
    View formula →
  13. 13.
    Quantitative Aptitude

    A can finish a job in 6 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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  14. 14.
    Quantitative Aptitude

    Find the average of these 10 numbers: 70, 89, 41, 26, 20, 58, 20, 52, 83, 67.

    Formula:Arithmetic Mean
    xˉ=∑xn\bar{x} = \dfrac{\sum x}{n}
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  15. 15.
    Quantitative Aptitude

    Find the HCF and LCM of 40 and 25.

    Formula:LCM & HCF
    LCM×HCF=a×b\text{LCM}\times\text{HCF} = a\times b
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  16. 16.
    Quantitative Aptitude

    Pipe A fills a tank in 14 hours and pipe B in 6 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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  17. 17.
    Quantitative Aptitude

    Find the HCF and LCM of 12 and 12.

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

    Divide £715 between two people in the ratio 7:6. 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}}
    View formula →
  19. 19.
    Quantitative Aptitude

    A can finish a job in 20 days and B in 13 days. Working together, how long will they take?

    Formula:Time & Work (combined)
    T=xyx+yT = \dfrac{xy}{x+y}
    View formula →
  20. 20.
    Quantitative Aptitude

    In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)

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