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UCAT · Practice Sheet 40

Sheet code: UCAT-S40 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Pipe A fills a tank in 11 hours and pipe B in 12 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
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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3.
Quantitative Aptitude
A invests £10,000 and B invests £9,000 for the same period. If the total profit is £17,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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4.
Quantitative Aptitude
Pipe A fills a tank in 6 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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5.
Quantitative Aptitude
What is 75% of 1,040?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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6.
Quantitative Aptitude
Find the compound interest on £14,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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7.
Quantitative Aptitude
A vehicle covers 248 km in 4 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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8.
Quantitative Aptitude
A can finish a job in 19 days and B in 13 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
Find the HCF and LCM of 38 and 36.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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10.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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11.
Quantitative Aptitude
A vehicle covers 112 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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12.
Quantitative Aptitude
The marked price of an item is £1,200. After a 10% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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13.
Quantitative Aptitude
A value changes from 500 to 400. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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14.
Quantitative Aptitude
A vehicle covers 756 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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15.
Quantitative Aptitude
Find the average of these 10 numbers: 22, 45, 78, 37, 86, 64, 81, 37, 77, 81.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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16.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 7?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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17.
Quantitative Aptitude
What is 15% of 400?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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18.
Quantitative Aptitude
Find the average of these 5 numbers: 86, 59, 30, 49, 74.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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19.
Quantitative Aptitude
A can finish a job in 11 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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20.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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