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TMUA · Practice Sheet 28

Sheet code: TMUA-S28 · 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 £25,000, 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
The sum of the ages of two people is 79 years, and one is 15 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 £18 and £98 per kg are mixed to give a mixture worth £80 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.
Mathematics
Evaluate ∫ from 0 to 3 of 1x^1 dx.
Formula:Definite Integral of a Power
$\int_{p}^{q} a x^{n}\,dx = \dfrac{a}{n+1}\big[x^{n+1}\big]_{p}^{q}$
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5.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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6.
Quantitative Aptitude
Pipe A fills a tank in 5 hours and pipe B in 6 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.
Mathematics
Find term number 3 of a geometric progression with first term 2 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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8.
Mathematics
In an arithmetic progression with first term 8 and common difference 2, find term number 25.
Formula:AP nth Term
$a_n = a + (n-1)d$
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9.
Quantitative Aptitude
Two varieties costing £16 and £71 per kg are mixed to give a mixture worth £51 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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10.
Mathematics
Find the sum of the first 4 terms of a GP with first term 4 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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11.
Quantitative Aptitude
Divide £270 between two people in the ratio 3:2. 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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12.
Mathematics
Find the sum of the first 23 terms of an AP with first term 10 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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13.
Quantitative Aptitude
A value changes from 500 to 700. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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14.
Quantitative Aptitude
Pipe A fills a tank in 13 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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15.
Mathematics
Find the sum of the first 15 terms of an AP with first term 15 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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16.
Mathematics
For the quadratic 5x² − 8x + 8 = 0, find the sum and product of its roots.
Formula:Vieta's Formulas (roots)
$\alpha+\beta=-\dfrac{b}{a},\;\alpha\beta=\dfrac{c}{a}$
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17.
Mathematics
Find term number 6 of a geometric progression with first term 5 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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18.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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19.
Quantitative Aptitude
Find the average of these 6 numbers: 51, 71, 35, 66, 50, 49.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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20.
Mathematics
In an arithmetic progression with first term 4 and common difference 1, find term number 8.
Formula:AP nth Term
$a_n = a + (n-1)d$
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