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GRE · Practice Sheet 44

Sheet code: GRE-S44 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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2.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 6?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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3.
Mathematics
Find the slope of the line through (8, -3) and (-6, 0).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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4.
Quantitative Aptitude
What is 30% of 180?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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5.
Quantitative Aptitude
A vehicle covers 190 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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6.
Quantitative Aptitude
Find the average of these 10 numbers: 44, 76, 51, 23, 54, 89, 21, 20, 61, 57.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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7.
Mathematics
Evaluate ∫ from 1 to 3 of 5x^3 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 term number 3 of a geometric progression with first term 2 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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9.
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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10.
Mathematics
In an arithmetic progression with first term 2 and common difference 4, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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11.
Quantitative Aptitude
Pipe A fills a tank in 7 hours and pipe B in 3 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
For the quadratic 5x² + 2x + 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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13.
Quantitative Aptitude
The marked price of an item is $800. After a 40% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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14.
Quantitative Aptitude
Find the average of these 6 numbers: 85, 59, 66, 90, 64, 67.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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15.
Mathematics
Find the distance between the points (-8, -4) and (-8, -5).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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16.
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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17.
Mathematics
Find the slope of the line through (-4, -4) and (7, -1).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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18.
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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19.
Quantitative Aptitude
A invests $7,000 and B invests $4,000 for the same period. If the total profit is $6,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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20.
Quantitative Aptitude
Divide $1,773 between two people in the ratio 5:4. 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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