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GRE · Practice Sheet 36

Sheet code: GRE-S36 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the slope of the line through (5, 0) and (-6, 3).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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2.
Mathematics
Find term number 3 of a geometric progression with first term 3 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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3.
Quantitative Aptitude
The sum of the ages of two people is 73 years, and one is 5 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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4.
Mathematics
Evaluate ∫ from 0 to 4 of 2x^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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5.
Quantitative Aptitude
A vehicle covers 192 km in 4 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: 57, 60, 25, 25, 86, 45, 87, 62, 42, 36.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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7.
Quantitative Aptitude
Pipe A fills a tank in 14 hours and pipe B in 4 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.
Quantitative Aptitude
The marked price of an item is $400. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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9.
Mathematics
Find the binomial coefficient C(8, 2) — the coefficient of x^2 in (1 + x)^8.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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10.
Quantitative Aptitude
Divide $1,701 between two people in the ratio 2:5. 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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11.
Quantitative Aptitude
A value changes from 900 to 1,125. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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12.
Mathematics
If f(x) = 5x³ + 6x² + 8x, find f′(3).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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13.
Mathematics
Find the slope of the line through (-1, -1) and (4, 8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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14.
Quantitative Aptitude
Divide $1,060 between two people in the ratio 7:3. 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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15.
Quantitative Aptitude
Find the HCF and LCM of 31 and 32.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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16.
Quantitative Aptitude
A invests $5,000 and B invests $6,000 for the same period. If the total profit is $30,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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17.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
Find the average of these 6 numbers: 64, 43, 69, 72, 69, 90.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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19.
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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20.
Quantitative Aptitude
Divide $1,650 between two people in the ratio 2:4. 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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