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GRE · Practice Sheet 1

Sheet code: GRE-S01 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 6 distinct objects? (Find ⁿᴄᵣ for n = 6, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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2.
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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3.
Quantitative Aptitude
An item is bought for $500 and sold for $700. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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4.
Quantitative Aptitude
A vehicle covers 111 km in 3 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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5.
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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6.
Quantitative Aptitude
Find the simple interest on $49,000 at 10% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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7.
Mathematics
Find the binomial coefficient C(9, 4) — the coefficient of x^4 in (1 + x)^9.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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8.
Mathematics
If f(x) = 2x³ + 1x² + 3x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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9.
Quantitative Aptitude
A invests $6,000 and B invests $10,000 for the same period. If the total profit is $36,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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10.
Mathematics
For the quadratic 5x² + 2x − 4 = 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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11.
Quantitative Aptitude
A can finish a job in 15 days and B in 8 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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12.
Mathematics
If f(x) = 5x³ + 5x² + 9x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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13.
Quantitative Aptitude
A invests $2,000 and B invests $6,000 for the same period. If the total profit is $29,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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14.
Quantitative Aptitude
In how many ways can 3 objects be arranged out of 8 distinct objects? (Find ⁿᴘᵣ for n = 8, r = 3.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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15.
Mathematics
Find the slope of the line through (2, 7) and (-7, -2).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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16.
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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17.
Quantitative Aptitude
The marked price of an item is $300. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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18.
Mathematics
If f(x) = 5x³ + 2x² + 5x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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19.
Quantitative Aptitude
Divide $2,366 between two people in the ratio 7:6. 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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20.
Mathematics
Find the sum of the first 9 terms of an AP with first term 18 and common difference 2.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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