UCAT · Practice Sheet 1

1. 1.

   Quantitative Aptitude

   A value changes from 400 to 280. Find the percentage decrease.

   Formula:Percentage Change

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

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2. 2.

   Quantitative Aptitude

   Find the compound interest on £20,000 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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3. 3.

   Quantitative Aptitude

   The sum of the ages of two people is 34 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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4. 4.

   Quantitative Aptitude

   Find the simple interest on £20,000 at 5% per annum for 2 year(s).

   Formula:Simple Interest

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

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5. 5.

   Quantitative Aptitude

   Divide £1,573 between two people in the ratio 6:5. 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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6. 6.

   Quantitative Aptitude

   A invests £5,000 and B invests £2,000 for the same period. If the total profit is £32,000, find A's share.

   Formula:Partnership (profit share)

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

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7. 7.

   Quantitative Aptitude

   Find the simple interest on £31,000 at 10% per annum for 4 year(s).

   Formula:Simple Interest

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

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8. 8.

   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

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

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9. 9.

   Quantitative Aptitude

   Divide £980 between two people in the ratio 7:3. 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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10. 10.

    Quantitative Aptitude

    Find the simple interest on £8,000 at 10% per annum for 5 year(s).

    Formula:Simple Interest

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

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11. 11.

    Quantitative Aptitude

    Divide £2,838 between two people in the ratio 6:5. 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

    In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)

    Formula:Permutations

    $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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13. 13.

    Quantitative Aptitude

    Find the average of these 6 numbers: 48, 51, 27, 58, 44, 30.

    Formula:Arithmetic Mean

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

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14. 14.

    Quantitative Aptitude

    What is 15% of 660?

    Formula:Percentage of a Number

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

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15. 15.

    Quantitative Aptitude

    A can finish a job in 13 days and B in 15 days. Working together, how long will they take?

    Formula:Time & Work (combined)

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

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16. 16.

    Quantitative Aptitude

    Two varieties costing £12 and £64 per kg are mixed to give a mixture worth £18 per kg. Find the mixing ratio.

    Formula:Alligation (Mixtures)

    $\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$

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17. 17.

    Quantitative Aptitude

    In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)

    Formula:Combinations

    $^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$

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18. 18.

    Quantitative Aptitude

    In how many ways can 4 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 4.)

    Formula:Permutations

    $^{n}P_{r} = \dfrac{n!}{(n-r)!}$

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19. 19.

    Quantitative Aptitude

    Find the simple interest on £14,000 at 6% per annum for 3 year(s).

    Formula:Simple Interest

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

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20. 20.

    Quantitative Aptitude

    A invests £9,000 and B invests £2,000 for the same period. If the total profit is £32,000, find A's share.

    Formula:Partnership (profit share)

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

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