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GMAT · Practice Sheet 28

Sheet code: GMAT-S28 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
A invests $9,000 and B invests $3,000 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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2.
Quantitative Aptitude
Find the simple interest on $19,000 at 4% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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3.
Mathematics
Evaluate ∫ from 0 to 5 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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4.
Mathematics
For the quadratic 3x² + 1x − 2 = 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
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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6.
Mathematics
Find the sum of the first 4 terms of a GP with first term 5 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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7.
Quantitative Aptitude
Pipe A fills a tank in 15 hours and pipe B in 5 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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8.
Mathematics
Find the binomial coefficient C(5, 2) — the coefficient of x^2 in (1 + x)^5.
Formula:Binomial Coefficient
$\binom{n}{r} = \dfrac{n!}{r!\,(n-r)!}$
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9.
Quantitative Aptitude
Pipe A fills a tank in 3 hours and pipe B in 12 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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10.
Mathematics
If f(x) = 1x³ + 1x² + 4x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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11.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 10?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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12.
Quantitative Aptitude
The sum of the ages of two people is 84 years, and one is 16 years older than the other. Find their ages.
Formula:Ages (linear equations)
$x + (x+d) = S$
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13.
Mathematics
Find the sum of the first 23 terms of an AP with first term 6 and common difference 8.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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14.
Mathematics
In an arithmetic progression with first term 3 and common difference 6, find term number 18.
Formula:AP nth Term
$a_n = a + (n-1)d$
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15.
Mathematics
Evaluate log base 2 of 32.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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16.
Mathematics
In an arithmetic progression with first term 2 and common difference 5, find term number 7.
Formula:AP nth Term
$a_n = a + (n-1)d$
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17.
Quantitative Aptitude
Find the HCF and LCM of 16 and 28.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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18.
Quantitative Aptitude
Find the simple interest on $33,000 at 12% per annum for 5 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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19.
Quantitative Aptitude
What is 50% of 860?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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20.
Quantitative Aptitude
A invests $7,000 and B invests $7,000 for the same period. If the total profit is $33,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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