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GMAT · Practice Sheet 29

Sheet code: GMAT-S29 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
Pipe A fills a tank in 15 hours and pipe B in 11 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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2.
Quantitative Aptitude
What is 75% of 380?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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3.
Quantitative Aptitude
Find the HCF and LCM of 38 and 36.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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4.
Mathematics
For the quadratic 4x² − 5x + 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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5.
Quantitative Aptitude
The sum of the ages of two people is 31 years, and one is 11 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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6.
Mathematics
Find term number 5 of a geometric progression with first term 2 and common ratio 3.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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7.
Mathematics
Find the distance between the points (8, -4) and (2, -8).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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8.
Quantitative Aptitude
An item is bought for $500 and sold for $550. 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 14 terms of an AP with first term 11 and common difference 5.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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10.
Quantitative Aptitude
An item is bought for $700 and sold for $805. Find the profit percentage.
Formula:Profit Percentage
$\text{Profit\%} = \dfrac{SP-CP}{CP}\times 100$
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11.
Quantitative Aptitude
The sum of the ages of two people is 27 years, and one is 7 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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12.
Mathematics
Find the slope of the line through (-7, 5) and (1, 4).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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13.
Quantitative Aptitude
The sum of the ages of two people is 80 years, and one is 10 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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14.
Mathematics
Evaluate ∫ from 0 to 3 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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15.
Mathematics
If f(x) = 5x³ + 6x² + 7x, find f′(4).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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16.
Quantitative Aptitude
Divide $847 between two people in the ratio 5:2. 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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17.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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18.
Quantitative Aptitude
A can finish a job in 6 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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19.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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20.
Quantitative Aptitude
A value changes from 600 to 660. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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