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SAT · Practice Sheet 36

Sheet code: SAT-US-S36 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Pipe A fills a tank in 15 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.
Mathematics
Find the distance between the points (4, 2) and (-2, -1).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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3.
Quantitative Aptitude
The sum of the ages of two people is 82 years, and one is 18 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Quantitative Aptitude
Two varieties costing $24 and $86 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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5.
Quantitative Aptitude
A value changes from 400 to 440. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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6.
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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7.
Mathematics
Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
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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9.
Mathematics
In an arithmetic progression with first term 11 and common difference 8, find term number 22.
Formula:AP nth Term
$a_n = a + (n-1)d$
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10.
Quantitative Aptitude
Find the HCF and LCM of 18 and 11.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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11.
Mathematics
For the quadratic 4x² − 2x + 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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12.
Mathematics
Evaluate log base 3 of 729.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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13.
Quantitative Aptitude
Divide $1,345 between two people in the ratio 2:3. 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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14.
Mathematics
If f(x) = 1x³ + 4x² + 3x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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15.
Quantitative Aptitude
Find the compound interest on $2,000 at 20% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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16.
Quantitative Aptitude
Divide $480 between two people in the ratio 3:3. 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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17.
Mathematics
Find the distance between the points (8, 2) and (-5, 8).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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18.
Mathematics
If f(x) = 3x³ + 2x² + 8x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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19.
Quantitative Aptitude
The sum of the ages of two people is 43 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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20.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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