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GMAT · Practice Sheet 47

Sheet code: GMAT-S47 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
If f(x) = 4x³ + 4x² + 2x, find f′(2).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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2.
Quantitative Aptitude
An item is bought for $700 and sold for $980. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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3.
Quantitative Aptitude
A can finish a job in 18 days and B in 17 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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4.
Mathematics
In an arithmetic progression with first term 19 and common difference 8, find term number 18.
Formula:AP nth Term
$a_n = a + (n-1)d$
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5.
Quantitative Aptitude
In how many ways can 4 objects be chosen from 7 distinct objects? (Find ⁿᴄᵣ for n = 7, r = 4.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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6.
Quantitative Aptitude
Divide $730 between two people in the ratio 4:6. 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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7.
Quantitative Aptitude
What is 60% of 1,080?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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8.
Mathematics
In an arithmetic progression with first term 11 and common difference 4, find term number 25.
Formula:AP nth Term
$a_n = a + (n-1)d$
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9.
Mathematics
Find the sum of the first 19 terms of an AP with first term 13 and common difference 6.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
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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11.
Mathematics
Evaluate ∫ from 2 to 4 of 5x^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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12.
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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13.
Mathematics
Find the binomial coefficient C(7, 4) — the coefficient of x^4 in (1 + x)^7.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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14.
Mathematics
For the quadratic 2x² − 7x + 7 = 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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15.
Quantitative Aptitude
A can finish a job in 16 days and B in 4 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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16.
Quantitative Aptitude
Find the average of these 5 numbers: 82, 67, 23, 79, 84.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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17.
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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18.
Mathematics
For the quadratic 2x² + 9x + 1 = 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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19.
Mathematics
In an arithmetic progression with first term 16 and common difference 6, find term number 23.
Formula:AP nth Term
$a_n = a + (n-1)d$
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20.
Mathematics
For the quadratic 4x² − 4x − 8 = 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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