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SAT · Practice Sheet 21

Sheet code: SAT-US-S21 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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2.
Mathematics
In an arithmetic progression with first term 11 and common difference 10, find term number 19.
Formula:AP nth Term
$a_n = a + (n-1)d$
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3.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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4.
Mathematics
Evaluate ∫ from 0 to 5 of 3x^2 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
Find the average of these 8 numbers: 32, 57, 47, 30, 73, 49, 39, 52.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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6.
Mathematics
Find the distance between the points (1, 1) and (-6, 6).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Quantitative Aptitude
Pipe A fills a tank in 15 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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8.
Quantitative Aptitude
An item is bought for $400 and sold for $560. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Quantitative Aptitude
The sum of the ages of two people is 54 years, and one is 8 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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10.
Mathematics
If f(x) = 3x³ + 6x² + 7x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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11.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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12.
Quantitative Aptitude
A vehicle covers 120 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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13.
Quantitative Aptitude
Pipe A fills a tank in 5 hours and pipe B in 7 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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14.
Mathematics
Find the sum of the first 9 terms of an AP with first term 2 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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15.
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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16.
Mathematics
Evaluate log base 2 of 16.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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17.
Mathematics
Find the distance between the points (0, -3) and (-7, -3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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18.
Quantitative Aptitude
A can finish a job in 15 days and B in 18 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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19.
Quantitative Aptitude
Find the average of these 6 numbers: 64, 57, 30, 54, 23, 70.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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20.
Quantitative Aptitude
A invests $3,000 and B invests $10,000 for the same period. If the total profit is $28,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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