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CAT · Practice Sheet 45

Sheet code: CAT-S45 · 20 questions

Name: ______________

Date: ______________

1.
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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2.
Mathematics
Evaluate log base 2 of 4.
Formula:Logarithm Evaluation
$\log_{b}(b^{k}) = k$
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3.
Mathematics
In an arithmetic progression with first term 15 and common difference 10, find term number 19.
Formula:AP nth Term
$a_n = a + (n-1)d$
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4.
Quantitative Aptitude
In how many ways can 3 objects be chosen from 9 distinct objects? (Find ⁿᴄᵣ for n = 9, r = 3.)
Formula:Combinations
$^{n}C_{r} = \dfrac{n!}{r!\,(n-r)!}$
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5.
Quantitative Aptitude
Find the average of these 10 numbers: 49, 56, 41, 85, 34, 90, 67, 71, 55, 38.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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6.
Quantitative Aptitude
The marked price of an item is ₹1,700. After a 20% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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7.
Quantitative Aptitude
A invests ₹8,000 and B invests ₹9,000 for the same period. If the total profit is ₹10,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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8.
Quantitative Aptitude
What is 20% of 560?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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9.
Quantitative Aptitude
Two varieties costing ₹39 and ₹71 per kg are mixed to give a mixture worth ₹64 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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10.
Quantitative Aptitude
A invests ₹9,000 and B invests ₹8,000 for the same period. If the total profit is ₹37,000, find A's share.
Formula:Partnership (profit share)
$\text{Share}_A = \text{Profit}\times\dfrac{A}{A+B}$
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11.
Quantitative Aptitude
Find the average of these 8 numbers: 70, 54, 87, 39, 57, 22, 68, 74.
Formula:Arithmetic Mean
$\bar{x} = \dfrac{\sum x}{n}$
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12.
Mathematics
Find term number 7 of a geometric progression with first term 2 and common ratio 2.
Formula:GP nth Term
$a_n = a\,r^{\,n-1}$
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13.
Mathematics
Find the sum of the first 6 terms of a GP with first term 6 and common ratio 3.
Formula:GP Sum of n Terms
$S_n = a\,\dfrac{r^{n}-1}{r-1}$
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14.
Quantitative Aptitude
Find the simple interest on ₹44,000 at 6% per annum for 1 year(s).
Formula:Simple Interest
$SI = \dfrac{P\times R\times T}{100}$
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15.
Mathematics
In an arithmetic progression with first term 11 and common difference 7, find term number 9.
Formula:AP nth Term
$a_n = a + (n-1)d$
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16.
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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17.
Quantitative Aptitude
A can finish a job in 11 days and B in 7 days. Working together, how long will they take?
Formula:Time & Work (combined)
$T = \dfrac{xy}{x+y}$
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18.
Quantitative Aptitude
What is 10% of 420?
Formula:Percentage of a Number
$\text{Value} = \dfrac{P}{100}\times N$
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19.
Quantitative Aptitude
Divide ₹890 between two people in the ratio 3:7. 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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20.
Quantitative Aptitude
The marked price of an item is ₹1,000. After a 15% discount, find the selling price.
Formula:Discount & Selling Price
$SP = MP\left(1-\dfrac{d}{100}\right)$
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