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GMAT · Practice Sheet 32

Sheet code: GMAT-S32 · 20 questions

Name: ______________

Date: ______________

1.
Mathematics
In an arithmetic progression with first term 10 and common difference 3, find term number 22.
Formula:AP nth Term
$a_n = a + (n-1)d$
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2.
Mathematics
Evaluate ∫ from 1 to 4 of 5x^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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3.
Quantitative Aptitude
A vehicle covers 486 km in 6 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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4.
Quantitative Aptitude
A can finish a job in 19 days and B in 21 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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5.
Quantitative Aptitude
Two varieties costing $19 and $91 per kg are mixed to give a mixture worth $85 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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6.
Mathematics
Find the sum of the first 14 terms of an AP with first term 9 and common difference 2.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
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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8.
Quantitative Aptitude
Two varieties costing $21 and $64 per kg are mixed to give a mixture worth $42 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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9.
Quantitative Aptitude
A can finish a job in 8 days and B in 16 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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10.
Mathematics
Find the distance between the points (-8, 3) and (5, -3).
Formula:Distance Between Two Points
$d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$
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11.
Quantitative Aptitude
Divide $2,541 between two people in the ratio 7:4. 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.
Quantitative Aptitude
Find the HCF and LCM of 36 and 17.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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13.
Mathematics
For the quadratic 1x² − 1x + 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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14.
Quantitative Aptitude
Find the average of these 10 numbers: 67, 41, 69, 77, 84, 24, 86, 46, 55, 69.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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15.
Quantitative Aptitude
A vehicle covers 170 km in 2 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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16.
Quantitative Aptitude
Find the compound interest on $15,000 at 20% per annum compounded annually for 2 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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17.
Quantitative Aptitude
A vehicle covers 384 km in 6 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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18.
Mathematics
Find the slope of the line through (4, -6) and (7, 2).
Formula:Slope of a Line
$m = \dfrac{y_2-y_1}{x_2-x_1}$
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19.
Mathematics
Find the sum of the first 3 terms of a GP with first term 1 and common ratio 2.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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20.
Quantitative Aptitude
Find the HCF and LCM of 18 and 36.
Formula:LCM & HCF
$\text{LCM}\times\text{HCF} = a\times b$
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