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GMAT · Practice Sheet 12

Sheet code: GMAT-S12 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
In how many ways can 2 objects be chosen from 10 distinct objects? (Find ⁿᴄᵣ for n = 10, r = 2.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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2.
Quantitative Aptitude
A can finish a job in 8 days and B in 19 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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3.
Quantitative Aptitude
A value changes from 200 to 150. Find the percentage decrease.
Formula:Percentage Change
$\%\,\text{change} = \dfrac{|new-old|}{old}\times 100$
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4.
Quantitative Aptitude
Pipe A fills a tank in 10 hours and pipe B in 14 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
The sum of the ages of two people is 82 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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6.
Quantitative Aptitude
Find the simple interest on $34,000 at 8% per annum for 4 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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7.
Mathematics
Find the slope of the line through (0, -8) and (-8, 8).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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8.
Quantitative Aptitude
The marked price of an item is $400. After a 30% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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9.
Mathematics
Find the sum of the first 7 terms of a GP with first term 1 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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10.
Quantitative Aptitude
Find the simple interest on $9,000 at 5% per annum for 6 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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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
Two varieties costing $38 and $83 per kg are mixed to give a mixture worth $69 per kg. Find the mixing ratio.
Formula:Alligation (Mixtures)
$\dfrac{q_1}{q_2} = \dfrac{p_2-m}{m-p_1}$
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13.
Mathematics
For the quadratic 2x² − 3x + 6 = 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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14.
Mathematics
In an arithmetic progression with first term 6 and common difference 1, find term number 15.
Formula:AP nth Term
$a_n = a + (n-1)d$
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15.
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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16.
Quantitative Aptitude
A vehicle covers 480 km in 8 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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17.
Quantitative Aptitude
A invests $3,000 and B invests $10,000 for the same period. If the total profit is $38,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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18.
Mathematics
If f(x) = 4x³ + 1x² + 4x, find f′(5).
Formula:Derivative of a Polynomial
$\dfrac{d}{dx}x^{n} = n\,x^{\,n-1}$
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19.
Quantitative Aptitude
A can finish a job in 9 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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20.
Quantitative Aptitude
Find the compound interest on $13,000 at 10% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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