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UCAT · Practice Sheet 7

Sheet code: UCAT-S07 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A can finish a job in 20 days and B in 6 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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2.
Quantitative Aptitude
The marked price of an item is £1,300. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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3.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 8 distinct objects? (Find ⁿᴄᵣ for n = 8, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Quantitative Aptitude
Find the average of these 8 numbers: 57, 88, 80, 46, 63, 39, 24, 42.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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5.
Quantitative Aptitude
A vehicle covers 284 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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6.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 11 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.
Quantitative Aptitude
A invests £10,000 and B invests £3,000 for the same period. If the total profit is £12,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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8.
Quantitative Aptitude
Divide £814 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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9.
Quantitative Aptitude
Find the compound interest on £20,000 at 10% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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10.
Quantitative Aptitude
Divide £1,290 between two people in the ratio 4:2. 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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11.
Quantitative Aptitude
A value changes from 900 to 810. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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12.
Quantitative Aptitude
A invests £2,000 and B invests £4,000 for the same period. If the total profit is £34,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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13.
Quantitative Aptitude
What is 10% of 120?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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14.
Quantitative Aptitude
Find the simple interest on £45,000 at 6% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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15.
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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16.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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17.
Quantitative Aptitude
Two varieties costing £31 and £88 per kg are mixed to give a mixture worth £41 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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18.
Quantitative Aptitude
A can finish a job in 7 days and B in 14 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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19.
Quantitative Aptitude
A vehicle covers 170 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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20.
Quantitative Aptitude
The sum of the ages of two people is 61 years, and one is 3 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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