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GRE · Practice Sheet 39

Sheet code: GRE-S39 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 5x³ + 2x² + 4x, find f′(1).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Quantitative Aptitude
The marked price of an item is $900. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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3.
Quantitative Aptitude
Pipe A fills a tank in 11 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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4.
Quantitative Aptitude
The sum of the ages of two people is 85 years, and one is 15 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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5.
Mathematics
Find the sum of the first 4 terms of a GP with first term 2 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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6.
Quantitative Aptitude
Find the average of these 5 numbers: 72, 35, 44, 23, 83.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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7.
Mathematics
Evaluate ∫ from 2 to 5 of 2x^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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8.
Mathematics
Find the slope of the line through (8, 5) and (-8, 5).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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9.
Mathematics
Find the sum of the first 15 terms of an AP with first term 10 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 4?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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11.
Mathematics
Evaluate log base 5 of 625.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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12.
Quantitative Aptitude
Pipe A fills a tank in 7 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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13.
Mathematics
Find the binomial coefficient C(10, 2) — the coefficient of x^2 in (1 + x)^10.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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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.
Mathematics
Find the binomial coefficient C(7, 3) — the coefficient of x^3 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Mathematics
Find the distance between the points (1, -1) and (6, 7).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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17.
Quantitative Aptitude
A invests $2,000 and B invests $8,000 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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18.
Quantitative Aptitude
What is 20% of 580?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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19.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 9 distinct objects? (Find ⁿᴘᵣ for n = 9, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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20.
Mathematics
Find the sum of the first 3 terms of a GP with first term 1 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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