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SAT · Practice Sheet 41

Sheet code: SAT-US-S41 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Quantitative Aptitude
The sum of the ages of two people is 68 years, and one is 14 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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3.
Quantitative Aptitude
A can finish a job in 12 days and B in 7 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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4.
Quantitative Aptitude
An item is bought for $500 and sold for $700. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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5.
Mathematics
For the quadratic 4x² − 2x + 6 = 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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6.
Mathematics
In an arithmetic progression with first term 10 and common difference 6, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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7.
Quantitative Aptitude
A invests $7,000 and B invests $4,000 for the same period. If the total profit is $9,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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8.
Mathematics
Find the slope of the line through (-3, -2) and (5, 6).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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9.
Quantitative Aptitude
Find the simple interest on $4,000 at 4% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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10.
Quantitative Aptitude
A invests $4,000 and B invests $6,000 for the same period. If the total profit is $35,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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11.
Quantitative Aptitude
Pipe A fills a tank in 10 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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12.
Mathematics
Find the binomial coefficient C(7, 2) — the coefficient of x^2 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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13.
Mathematics
Find the distance between the points (7, -2) and (2, -2).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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14.
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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15.
Quantitative Aptitude
A can finish a job in 14 days and B in 6 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 300 to 345. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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17.
Quantitative Aptitude
Find the average of these 5 numbers: 53, 39, 71, 84, 55.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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18.
Quantitative Aptitude
A vehicle covers 312 km in 6 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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19.
Mathematics
For the quadratic 1x² − 6x + 9 = 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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20.
Mathematics
If f(x) = 5x³ + 6x² + 6x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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