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CAT · Practice Sheet 28

Sheet code: CAT-S28 · 20 questions

Name: ______________

Date: ______________

1.
Quantitative Aptitude
What is 60% of 1,040?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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2.
Quantitative Aptitude
Two varieties costing ₹18 and ₹60 per kg are mixed to give a mixture worth ₹28 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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3.
Mathematics
For the quadratic 1x² − 8x − 1 = 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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4.
Quantitative Aptitude
Find the compound interest on ₹10,000 at 20% per annum compounded annually for 3 years.
Formula:Compound Interest
$A = P\left(1+\dfrac{R}{100}\right)^{T}$
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5.
Mathematics
In an arithmetic progression with first term 6 and common difference 1, find term number 18.
Formula:AP nth Term
$a_n = a + (n-1)d$
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6.
Mathematics
Find the sum of the first 16 terms of an AP with first term 2 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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7.
Mathematics
In an arithmetic progression with first term 16 and common difference 10, find term number 30.
Formula:AP nth Term
$a_n = a + (n-1)d$
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8.
Mathematics
Find the sum of the first 5 terms of a GP with first term 5 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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9.
Mathematics
In an arithmetic progression with first term 9 and common difference 9, find term number 17.
Formula:AP nth Term
$a_n = a + (n-1)d$
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10.
Quantitative Aptitude
Two fair dice are rolled. What is the probability that the sum of the numbers is 9?
Formula:Probability (two dice)
$P = \dfrac{\text{favourable}}{\text{total}}$
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11.
Quantitative Aptitude
A vehicle covers 285 km in 5 hours. Find its average speed.
Formula:Speed, Distance & Time
$\text{Speed} = \dfrac{\text{Distance}}{\text{Time}}$
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12.
Quantitative Aptitude
Pipe A fills a tank in 12 hours and pipe B in 10 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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13.
Quantitative Aptitude
A invests ₹3,000 and B invests ₹9,000 for the same period. If the total profit is ₹16,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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14.
Quantitative Aptitude
A can finish a job in 5 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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15.
Quantitative Aptitude
Find the average of these 10 numbers: 37, 44, 23, 53, 38, 22, 61, 78, 76, 39.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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16.
Quantitative Aptitude
A can finish a job in 14 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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17.
Quantitative Aptitude
Pipe A fills a tank in 6 hours and pipe B in 8 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
Find the compound interest on ₹11,000 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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19.
Quantitative Aptitude
Pipe A fills a tank in 14 hours and pipe B in 9 hours. If both are opened together, how long to fill the tank?
Formula:Pipes & Cisterns
$T = \dfrac{xy}{x+y}$
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20.
Mathematics
Find the sum of the first 18 terms of an AP with first term 20 and common difference 1.
Formula:AP Sum of n Terms
$S_n = \dfrac{n}{2}\,[2a+(n-1)d]$
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