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GMAT · Practice Sheet 24

Sheet code: GMAT-S24 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A invests $3,000 and B invests $2,000 for the same period. If the total profit is $8,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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2.
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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3.
Mathematics
Find the sum of the first 5 terms of an AP with first term 3 and common difference 9.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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4.
Quantitative Aptitude
Find the compound interest on $5,000 at 10% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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5.
Quantitative Aptitude
In how many ways can 2 objects be arranged out of 7 distinct objects? (Find ⁿᴘᵣ for n = 7, r = 2.)
Formula:Permutations
$^{n}P_{r} = \dfrac{n!}{(n-r)!}$
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6.
Mathematics
Find the distance between the points (7, 3) and (-7, -6).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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7.
Quantitative Aptitude
A can finish a job in 20 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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8.
Mathematics
In an arithmetic progression with first term 20 and common difference 10, find term number 30.
Formula:AP nth Term
$a_n = a + (n-1)d$
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9.
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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10.
Quantitative Aptitude
A value changes from 900 to 1,035. Find the percentage increase.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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11.
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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12.
Quantitative Aptitude
Divide $1,869 between two people in the ratio 2:5. 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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13.
Quantitative Aptitude
What is 75% of 500?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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14.
Quantitative Aptitude
The sum of the ages of two people is 57 years, and one is 5 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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15.
Mathematics
Find the sum of the first 3 terms of a GP with first term 4 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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16.
Mathematics
Evaluate ∫ from 0 to 3 of 3x^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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17.
Quantitative Aptitude
What is 25% of 880?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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18.
Mathematics
In an arithmetic progression with first term 15 and common difference 1, find term number 30.
Formula:AP nth Term
$a_n = a + (n-1)d$
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19.
Mathematics
For the quadratic 1x² − 7x + 5 = 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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20.
Quantitative Aptitude
Find the compound interest on $6,000 at 10% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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