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UCAT · Practice Sheet 22

Sheet code: UCAT-S22 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Pipe A fills a tank in 4 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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2.
Quantitative Aptitude
The sum of the ages of two people is 45 years, and one is 13 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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3.
Quantitative Aptitude
Two varieties costing £31 and £60 per kg are mixed to give a mixture worth £52 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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4.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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5.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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6.
Quantitative Aptitude
A invests £4,000 and B invests £10,000 for the same period. If the total profit is £37,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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7.
Quantitative Aptitude
A can finish a job in 6 days and B in 8 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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8.
Quantitative Aptitude
A value changes from 800 to 760. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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9.
Quantitative Aptitude
An item is bought for £200 and sold for £250. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Quantitative Aptitude
A value changes from 700 to 350. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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11.
Quantitative Aptitude
Two varieties costing £15 and £69 per kg are mixed to give a mixture worth £30 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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12.
Quantitative Aptitude
A value changes from 400 to 560. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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13.
Quantitative Aptitude
The marked price of an item is £500. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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14.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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15.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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16.
Quantitative Aptitude
Divide £1,944 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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17.
Quantitative Aptitude
A can finish a job in 16 days and B in 10 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
Find the HCF and LCM of 9 and 30.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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19.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Quantitative Aptitude
What is 15% of 860?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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