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GMAT · Practice Sheet 33

Sheet code: GMAT-S33 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
Evaluate ∫ from 2 to 5 of 1x^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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2.
Quantitative Aptitude
Find the average of these 6 numbers: 61, 28, 87, 41, 40, 22.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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3.
Quantitative Aptitude
The marked price of an item is $1,300. After a 10% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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4.
Mathematics
Evaluate ∫ from 1 to 4 of 1x^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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5.
Quantitative Aptitude
Find the simple interest on $22,000 at 4% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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6.
Mathematics
For the quadratic 5x² − 7x + 3 = 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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7.
Quantitative Aptitude
A can finish a job in 15 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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8.
Quantitative Aptitude
What is 60% of 980?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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9.
Quantitative Aptitude
Find the average of these 8 numbers: 25, 65, 41, 78, 47, 57, 42, 64.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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10.
Mathematics
In an arithmetic progression with first term 1 and common difference 10, find term number 14.
Formula:AP nth Term
$a_n = a + (n-1)d$
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11.
Quantitative Aptitude
Divide $2,650 between two people in the ratio 5:5. 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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12.
Mathematics
Evaluate log base 10 of 1,000.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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13.
Quantitative Aptitude
Find the average of these 8 numbers: 57, 52, 22, 82, 79, 53, 51, 78.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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14.
Quantitative Aptitude
A value changes from 400 to 320. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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15.
Mathematics
Find term number 4 of a geometric progression with first term 5 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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16.
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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17.
Quantitative Aptitude
A can finish a job in 12 days and B in 10 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
The marked price of an item is $400. After a 50% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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19.
Quantitative Aptitude
Divide $1,064 between two people in the ratio 6:2. 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
For the quadratic 1x² + 7x − 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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