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GRE · Practice Sheet 25

Sheet code: GRE-S25 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Find the slope of the line through (1, -8) and (4, 8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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2.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 5 distinct objects? (Find ⁿᴘᵣ for n = 5, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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3.
Mathematics
Find the distance between the points (-4, 5) and (-4, -8).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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4.
Quantitative Aptitude
A invests $4,000 and B invests $2,000 for the same period. If the total profit is $33,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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5.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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6.
Mathematics
Find the distance between the points (-1, 6) and (-7, 0).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Mathematics
Find the binomial coefficient C(5, 3) — the coefficient of x^3 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Quantitative Aptitude
An item is bought for $800 and sold for $1,200. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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9.
Mathematics
Find the sum of the first 8 terms of an AP with first term 6 and common difference 10.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Quantitative Aptitude
Find the simple interest on $46,000 at 4% per annum for 2 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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11.
Mathematics
Evaluate ∫ from 1 to 5 of 5x^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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12.
Quantitative Aptitude
A can finish a job in 5 days and B in 12 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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13.
Quantitative Aptitude
A vehicle covers 783 km in 9 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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14.
Quantitative Aptitude
Divide $427 between two people in the ratio 3:4. 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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15.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 5 distinct objects? (Find ⁿᴄᵣ for n = 5, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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16.
Mathematics
Find the slope of the line through (8, -7) and (1, 4).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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17.
Mathematics
Evaluate log base 3 of 9.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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18.
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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19.
Quantitative Aptitude
Find the compound interest on $17,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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20.
Quantitative Aptitude
The marked price of an item is $600. After a 5% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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