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UCAT · Practice Sheet 50

Sheet code: UCAT-S50 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A invests £5,000 and B invests £5,000 for the same period. If the total profit is £21,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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2.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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3.
Quantitative Aptitude
An item is bought for £300 and sold for £375. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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4.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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5.
Quantitative Aptitude
Find the simple interest on £27,000 at 4% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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6.
Quantitative Aptitude
What is 40% of 1,020?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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7.
Quantitative Aptitude
Find the simple interest on £21,000 at 10% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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8.
Quantitative Aptitude
A invests £3,000 and B invests £10,000 for the same period. If the total profit is £31,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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9.
Quantitative Aptitude
A vehicle covers 324 km in 6 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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10.
Quantitative Aptitude
A can finish a job in 5 days and B in 20 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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11.
Quantitative Aptitude
Two varieties costing £21 and £88 per kg are mixed to give a mixture worth £82 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
Two fair dice are rolled. What is the probability that the sum of the numbers is 5?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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13.
Quantitative Aptitude
The sum of the ages of two people is 75 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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14.
Quantitative Aptitude
Divide £1,251 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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15.
Quantitative Aptitude
A can finish a job in 20 days and B in 22 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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16.
Quantitative Aptitude
A value changes from 600 to 690. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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17.
Quantitative Aptitude
Find the HCF and LCM of 28 and 13.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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18.
Quantitative Aptitude
What is 30% of 380?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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19.
Quantitative Aptitude
Find the average of these 10 numbers: 84, 49, 23, 41, 85, 56, 37, 54, 53, 81.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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20.
Quantitative Aptitude
Divide £1,680 between two people in the ratio 7:7. 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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