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GRE · Practice Sheet 35

Sheet code: GRE-S35 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 3x³ + 4x² + 8x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Quantitative Aptitude
Two varieties costing $17 and $74 per kg are mixed to give a mixture worth $69 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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3.
Quantitative Aptitude
A can finish a job in 10 days and B in 9 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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4.
Quantitative Aptitude
The marked price of an item is $1,900. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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5.
Mathematics
For the quadratic 1x² + 5x + 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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6.
Quantitative Aptitude
An item is bought for $600 and sold for $690. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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7.
Mathematics
Find the sum of the first 7 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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8.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 13 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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9.
Quantitative Aptitude
An item is bought for $400 and sold for $440. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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10.
Quantitative Aptitude
A invests $7,000 and B invests $9,000 for the same period. If the total profit is $14,000, 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
A value changes from 900 to 855. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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12.
Quantitative Aptitude
Two varieties costing $16 and $86 per kg are mixed to give a mixture worth $40 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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13.
Mathematics
Evaluate ∫ from 1 to 5 of 2x^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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14.
Quantitative Aptitude
What is 15% of 220?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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15.
Quantitative Aptitude
Find the average of these 6 numbers: 69, 77, 59, 70, 20, 78.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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16.
Quantitative Aptitude
The marked price of an item is $900. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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17.
Mathematics
Find the distance between the points (7, 7) and (5, 4).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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18.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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19.
Quantitative Aptitude
The sum of the ages of two people is 69 years, and one is 17 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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20.
Quantitative Aptitude
Divide $2,710 between two people in the ratio 5:5. 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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