UCAT · Practice Sheet 4

1. 1.

   Quantitative Aptitude

   Find the average of these 8 numbers: 51, 23, 50, 67, 77, 60, 59, 44.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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2. 2.

   Quantitative Aptitude

   A value changes from 900 to 540. Find the percentage decrease.

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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3. 3.

   Quantitative Aptitude

   The sum of the ages of two people is 60 years, and one is 6 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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4. 4.

   Quantitative Aptitude

   Divide £1,674 between two people in the ratio 3:6. How much does each receive?

   Formula:Sharing in a Ratio

   $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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5. 5.

   Quantitative Aptitude

   What is 40% of 1,040?

   Formula:Percentage of a Number

   $\text{Value} = \dfrac{P}{100}\times N$

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6. 6.

   Quantitative Aptitude

   Pipe A fills a tank in 8 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?

   Formula:Pipes & Cisterns

   $T = \dfrac{xy}{x+y}$

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7. 7.

   Quantitative Aptitude

   The sum of the ages of two people is 72 years, and one is 10 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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8. 8.

   Quantitative Aptitude

   Find the average of these 6 numbers: 63, 34, 63, 27, 20, 50.

   Formula:Arithmetic Mean

   $\bar{x} = \dfrac{\sum x}{n}$

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9. 9.

   Quantitative Aptitude

   The sum of the ages of two people is 75 years, and one is 19 years older than the other. Find their ages.

   Formula:Ages (linear equations)

   $x + (x+d) = S$

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10. 10.

    Quantitative Aptitude

    A vehicle covers 395 km in 5 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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11. 11.

    Quantitative Aptitude

    Divide £2,176 between two people in the ratio 3:5. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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12. 12.

    Quantitative Aptitude

    The sum of the ages of two people is 41 years, and one is 9 years older than the other. Find their ages.

    Formula:Ages (linear equations)

    $x + (x+d) = S$

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13. 13.

    Quantitative Aptitude

    A vehicle covers 240 km in 3 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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14. 14.

    Quantitative Aptitude

    A value changes from 800 to 1,200. Find the percentage increase.

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$

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15. 15.

    Quantitative Aptitude

    A vehicle covers 138 km in 2 hours. Find its average speed.

    Formula:Speed, Distance & Time

    $\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$

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16. 16.

    Quantitative Aptitude

    A invests £9,000 and B invests £2,000 for the same period. If the total profit is £28,000, find A's share.

    Formula:Partnership (profit share)

    $\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$

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17. 17.

    Quantitative Aptitude

    Divide £2,684 between two people in the ratio 5:6. How much does each receive?

    Formula:Sharing in a Ratio

    $\text{Share} = \text{Total}\times\dfrac{\text{part}}{\text{sum of parts}}$

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18. 18.

    Quantitative Aptitude

    Find the simple interest on £23,000 at 4% per annum for 6 year(s).

    Formula:Simple Interest

    $SI = \dfrac{P\times R\times T}{100}$

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19. 19.

    Quantitative Aptitude

    Find the compound interest on £15,000 at 20% per annum compounded annually for 2 years.

    Formula:Compound Interest

    $A = P\left(1+\dfrac{R}{100}\right)^{T}$

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20. 20.

    Quantitative Aptitude

    An item is bought for £900 and sold for £1,035. Find the profit percentage.

    Formula:Profit Percentage

    $\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$

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