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UCAT · Practice Sheet 5

Sheet code: UCAT-S05 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Find the HCF and LCM of 28 and 12.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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2.
Quantitative Aptitude
What is 75% of 1,200?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Quantitative Aptitude
Pipe A fills a tank in 9 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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4.
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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5.
Quantitative Aptitude
Two varieties costing £40 and £74 per kg are mixed to give a mixture worth £58 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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6.
Quantitative Aptitude
The marked price of an item is £2,000. After a 25% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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7.
Quantitative Aptitude
An item is bought for £600 and sold for £840. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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8.
Quantitative Aptitude
Divide £2,743 between two people in the ratio 6:7. 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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9.
Quantitative Aptitude
A can finish a job in 13 days and B in 4 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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10.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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11.
Quantitative Aptitude
Pipe A fills a tank in 9 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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12.
Quantitative Aptitude
Divide £1,160 between two people in the ratio 6:4. 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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13.
Quantitative Aptitude
Find the average of these 5 numbers: 89, 29, 25, 71, 83.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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14.
Quantitative Aptitude
Divide £3,135 between two people in the ratio 7:4. 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 value changes from 800 to 640. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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16.
Quantitative Aptitude
The sum of the ages of two people is 77 years, and one is 19 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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17.
Quantitative Aptitude
Find the compound interest on £2,000 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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18.
Quantitative Aptitude
A invests £7,000 and B invests £4,000 for the same period. If the total profit is £40,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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19.
Quantitative Aptitude
Two varieties costing £37 and £87 per kg are mixed to give a mixture worth £61 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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20.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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