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SAT · Practice Sheet 32

Sheet code: SAT-US-S32 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the sum of the first 5 terms of a GP with first term 6 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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2.
Quantitative Aptitude
An item is bought for $200 and sold for $230. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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3.
Quantitative Aptitude
The sum of the ages of two people is 53 years, and one is 19 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Mathematics
Find the binomial coefficient C(10, 4) — the coefficient of x^4 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
A invests $7,000 and B invests $6,000 for the same period. If the total profit is $11,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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6.
Mathematics
Find the distance between the points (6, 8) and (2, -1).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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8.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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9.
Mathematics
Find the sum of the first 16 terms of an AP with first term 11 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Mathematics
Evaluate log base 3 of 27.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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11.
Quantitative Aptitude
Pipe A fills a tank in 12 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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12.
Mathematics
If f(x) = 5x³ + 5x² + 2x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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13.
Quantitative Aptitude
A can finish a job in 13 days and B in 19 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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14.
Mathematics
In an arithmetic progression with first term 4 and common difference 9, find term number 22.
Formula:AP nth Term
$a_n = a + (n-1)d$
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15.
Quantitative Aptitude
In how many ways can 4 objects be arranged out of 6 distinct objects? (Find ⁿᴘᵣ for n = 6, r = 4.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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16.
Mathematics
Find term number 3 of a geometric progression with first term 5 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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17.
Quantitative Aptitude
Two varieties costing $29 and $84 per kg are mixed to give a mixture worth $76 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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18.
Mathematics
Find the distance between the points (-3, 3) and (2, 6).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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19.
Mathematics
Evaluate ∫ from 0 to 4 of 3x^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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20.
Mathematics
Find the distance between the points (-3, -1) and (2, -4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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