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SAT · Practice Sheet 34

Sheet code: SAT-US-S34 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Two varieties costing $33 and $69 per kg are mixed to give a mixture worth $42 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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2.
Mathematics
In an arithmetic progression with first term 5 and common difference 8, find term number 24.
Formula:AP nth Term
$a_n = a + (n-1)d$
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3.
Quantitative Aptitude
What is 50% of 780?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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4.
Quantitative Aptitude
A invests $5,000 and B invests $7,000 for the same period. If the total profit is $22,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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5.
Quantitative Aptitude
Divide $774 between two people in the ratio 4:5. 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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6.
Mathematics
If f(x) = 1x³ + 6x² + 7x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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7.
Quantitative Aptitude
Pipe A fills a tank in 11 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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8.
Mathematics
Find the distance between the points (-8, -4) and (-6, 6).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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9.
Quantitative Aptitude
Find the average of these 10 numbers: 55, 45, 81, 48, 45, 36, 90, 28, 42, 85.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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10.
Mathematics
Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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11.
Mathematics
If f(x) = 5x³ + 4x² + 1x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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12.
Quantitative Aptitude
The marked price of an item is $1,400. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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13.
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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14.
Mathematics
Find the sum of the first 13 terms of an AP with first term 2 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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15.
Mathematics
Evaluate log base 3 of 81.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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16.
Mathematics
For the quadratic 1x² − 1x − 4 = 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
Evaluate ∫ from 0 to 3 of 4x^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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18.
Mathematics
Find the sum of the first 7 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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19.
Mathematics
For the quadratic 1x² + 8x + 0 = 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.
Quantitative Aptitude
Find the average of these 5 numbers: 59, 31, 82, 48, 74.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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