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121

CAT 2021 Set-1 | Quantitative Aptitude | Question: 20
A circle of diameter $8 \; \text{inches}$ is inscribed in a triangle $\text{ABC}$ where $\angle \text{ABC} = 90^{\circ}.$ If $\text{BC} = 10 \; \text{inches}$ then the area of the triangle in $\text{square inches}$ is

soujanyareddy13 asked in Quantitative Aptitude Jan 19, 2022

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122

CAT 2021 Set-1 | Quantitative Aptitude | Question: 21
Onion is sold for $5$ consecutive months at the rate of $\text{Rs}\; 10, 20, 25, 25,$ and $50 \; \text{per kg},$ respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that ... $5 \; \text{months}$ is closest to $18$ $16$ $26$ $20$

soujanyareddy13 asked in Quantitative Aptitude Jan 19, 2022

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123

CAT 2021 Set-1 | Quantitative Aptitude | Question: 22
Identical chocolate pieces are sold in boxes of two sizes, small and large. The large box is sold for twice the price of the small box. If the selling price $\text{per gram}$ of chocolate in the large box is $12 \%$ less than that in ... the weight of chocolate in the large box exceeds that in the small box is nearest to $135$ $127$ $144$ $124$

soujanyareddy13 asked in Quantitative Aptitude Jan 19, 2022

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124

CAT 2020 Set-3 | Question: 51
If $\log_{a} 30 = \text{A}, \log_{a} (5/3) = – \text{B} $ and $\log_{2} a = 1/3,$ then $\log_{3}a $ equals $ \frac{2}{\text{A + B}} \;– 3 $ $ \frac{\text{A + B} - 3}{2} $ $ \frac{2}{\text{A + B} – 3} $ $ \frac{\text{A + B}}{2}\; – 3 $

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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125

CAT 2020 Set-3 | Question: 52
Dick is thrice as old as Tom and Harry is twice as old as Dick. If Dick’s age is $1$ year less than the average age of all three, then Harry’s age, in years, is

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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126

CAT 2020 Set-3 | Question: 53
$\text{A}$ and $\text{B}$ are two railway stations $90 \; \text{km}$ apart. A train leaves $\text{A}$ at $9:00 \; \text{am},$ heading towards $\text{B}$ at a speed of $40 \; \text{km/hr}.$ Another train leaves $\text{B}$ at $10:30 \; \text{am},$ heading towards ... each other at $ 11:45 \; \text{am} $ $ 10:45 \; \text{am} $ $ 11:20 \; \text{am} $ $ 11:00 \; \text{am} $

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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127

CAT 2020 Set-3 | Question: 54
Let $k$ be a constant. The equations $kx + y= 3$ and $4x + ky= 4$ have a unique solution if and only if $|k| \neq 2$ $|k| = 2$ $k \neq 2$ $k= 2$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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128

CAT 2020 Set-3 | Question: 55
If $x_{1} = \;– 1$ and $x_{m} = x_{m+1} + (m + 1)$ for every positive integer $m, $ then $x_{100}$ equals $ – 5151 $ $ – 5150 $ $ – 5051 $ $ – 5050 $

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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129

CAT 2020 Set-3 | Question: 56
Vimla starts for office every day at $9 \; \text{am}$ and reaches exactly on time if she drives at her usual speed of $40 \; \text{km/hr}.$ She is late by $6 \; \text{minutes}$ if she drives at $35 \; \text{km/hr}.$ One day, she covers ... speed, in $\text{km/hr},$ at which she should drive the remaining distance to reach office exactly on time is $29$ $27$ $28$ $26$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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130

CAT 2020 Set-3 | Question: 57
A man buys $35 \; \text{kg}$ of sugar and sets a marked price in order to make a $20\%$ profit. He sells $5 \; \text{kg}$ at this price, and $15 \; \text{kg}$ at a $10\%$ discount. Accidentally, $3 \; \text{kg}$ of sugar is wasted. He sells ... raising the marked price by $p$ percent so as to make an overall profit of $15\%.$ Then $p$ is nearest to $31$ $22$ $35$ $25$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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131

CAT 2020 Set-3 | Question: 58
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$ $15.9375$ $3$ $14.0625$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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132

CAT 2020 Set-3 | Question: 59
If $\text{a,b,c}$ are non-zero and $14^{a} = 36^{b} = 84^{c},$ then $6b \left( \frac{1}{c} \;– \frac{1}{a} \right)$ is equal to

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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133

CAT 2020 Set-3 | Question: 60
A contractor agreed to construct a $6 \; \text{km}$ road in $200 \; \text{days}.$ He employed $140$ persons for the work. After $60 \; \text{days},$ he realized that only $1.5 \; \text{km}$ road has been completed. How many additional people would he need to employ in order to finish the work exactly on time $?$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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134

CAT 2020 Set-3 | Question: 61
Let $\text{m}$ and $\text{n}$ be positive integers, If $x^{2} + mx + 2n = 0$ and $x^{2} + 2nx + m = 0$ have real roots, then the smallest possible value of $m + n$ is $7$ $8$ $5$ $6$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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135

CAT 2020 Set-3 | Question: 62
A person invested a certain amount of money at $10\%$ annual interest, compounded half-yearly. After one and a half years, the interest and principal together became $\text{Rs} \; 18522.$ The amount, in rupees, that the person had invested is

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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136

CAT 2020 Set-3 | Question: 63
Anil, Sunil, and Ravi run along a circular path of length $3 \; \text{km},$ starting from the same point at the same time, and going in the clockwise direction. If they run at speed of $15 \; \text{km/hr}, 10 \; \text{km/hr},$ ... will Ravi have run when Anil and Sunil meet again for the first time at the starting point $?$ $4.2$ $5.2$ $4.8$ $4.6$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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137

CAT 2020 Set-3 | Question: 64
The area, in $\text{sq. units},$ enclosed by the lines $x = 2, y = |x – 2| + 4,$ the X-axis and the Y-axis is equal to $8$ $12$ $10$ $6$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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138

CAT 2020 Set-3 | Question: 65
The vertices of a triangle are $(0,0), (4,0)$ and $(3,9).$ The area of the circle passing through these three points is $\frac{14 \pi}{3}$ $\frac{12 \pi}{5}$ $\frac{123 \pi}{7}$ $\frac{205 \pi}{9}$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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139

CAT 2020 Set-3 | Question: 66
How many integers in the set $\{ 100, 101, 102, \dots, 999\}$ have at least one digit repeated $?$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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140

CAT 2020 Set-3 | Question: 67
Let $\text{N}, x$ and $y$ be positive integers such that $N = x + y, 2 < x < 10$ and $14 < y < 23.$ If $\text{N} > 25,$ then how many distinct values are possible for $\text{N} ?$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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141

CAT 2020 Set-3 | Question: 68
The points $(2,1)$ and $( – 3, – 4)$ are opposite vertices of a parallelogram. If the other two vertices lie on the line $x + 9y + c = 0,$ then $\text{c}$ is $12$ $14$ $13$ $15$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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142

CAT 2020 Set-3 | Question: 69
How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$ $2017$ $2019$ $2020$ $2018$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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143

CAT 2020 Set-3 | Question: 70
In a trapezium $\text{ABCD},\; \text{AB}$ is parallel to $\text{DC}, \; \text{BC}$ is perpendicular to $\text{DC}$ and $\angle \text{BAD} = 45^{\circ}.$ If $\text{DC} = 5 \; \text{cm}, \; \text{BC} = 4 \; \text{cm},$ the area of the trapezium in $\text{sq. cm}$ is

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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144

CAT 2020 Set-3 | Question: 71
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$ $40$ $42$ $43$ $41$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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145

CAT 2020 Set-3 | Question: 72
Two alcohol solutions, $\text{A}$ and $\text{B},$ are mixed in the proportion $1:3$ by volume. The volume of the mixture is then doubled by adding solution $\text{A}$ such that the resulting mixture has $72\%$ alcohol. If solution $\text{A}$ has $60\%$ alcohol, then the percentage of alcohol in solution $\text{B}$ is $94\%$ $92\%$ $90\%$ $89\%$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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146

CAT 2020 Set-3 | Question: 73
$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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147

CAT 2020 Set-3 | Question: 74
A batsman played $n + 2$ innings and got out on all occasions. His average score in these $n + 2$ innings was $29$ runs and he scored $38$ and $15$ runs in the last two innings. The batsman scored less than $38$ runs in each of the first $n$ innings. ... average score was $30$ runs and lowest score was $x$ runs. The smallest possible value of $x$ is $2$ $3$ $4$ $1$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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148

CAT 2020 Set-3 | Question: 75
In the final examination, Bishnu scored $52\%$ and Asha scored $64\%.$ The marks obtained by Bishnu is $23$ less, and that by Asha is $34$ more than the marks obtained by Ramesh. The marks obtained by Geeta, who scored $84\%,$ is $439$ $399$ $357$ $417$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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149

CAT 2020 Set-3 | Question: 76
Let $\text{m}$ and $\text{n}$ be natural numbers such that $\text{n}$ is even and $0.2 < \frac{m}{20}, \frac{n}{m}, \frac{n}{11} < 0 \cdot 5.$ Then $m – 2n$ equals $3$ $4$ $1$ $2$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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150

CAT 2020 Set-2 | Question: 51
The sum of the perimeters of an equilateral triangle and a rectangle is $90 \; \text{cm}.$ The area, $\text{T},$ of the triangle and the area, $\text{R},$ of the rectangle, both in $\text{sq cm},$ satisfy the ... of the rectangle are in the ratio $1:3,$ then the length, in cm, of the longer side of the rectangle, is $24$ $27$ $21$ $18$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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151

CAT 2020 Set-2 | Question: 52
In May, John bought the same amount of rice and the same amount of wheat as he had bought in April, but spent $₹150$ more due to price increase of rice and wheat by $20\%$ and $12\%,$ respectively. If John had spent $₹450$ on rice in April, then how much did he spend on wheat in May $?$ $₹580$ $₹570$ $₹560$ $₹590$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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152

CAT 2020 Set-2 | Question: 53
In a car race, car $\text{A}$ beats car $\text{B}$ by $45 \; \text{km},$ car $\text{B}$ beats car $\text{C}$ by $50 \; \text{km},$ and car $\text{A}$ beats car $\text{C}$ by $90\;\text{km}.$ The distance $\text{(in km)}$ over which the race has been conducted is $500$ $475$ $550$ $450$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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153

CAT 2020 Set-2 | Question: 54
John takes twice as much time as Jack to finish a job. Jack and Jim together take one-thirds of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John takes three days more than that taken by three of them working together. In how many days will Jim finish the job working alone $?$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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2 votes

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154

CAT 2020 Set-2 | Question: 55
Let the $\text{m-th}$ and $\text{n-th}$ terms of a geometric progression be $\frac{3}{4}$ and $12,$ respectively, where $\text{m < n}.$ If the common ratio of the progression is an integer $\textsf{r},$ then the smallest possible value of $\textsf{r+n-m}$ is $ - 2$ $2$ $6$ $ – 4$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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155

CAT 2020 Set-2 | Question: 56
If $\textsf{x}$ and $\textsf{y}$ are positive real numbers satisfying $\textsf{x+y = 102},$ then the minimum possible value of $\textsf{2601} \left( 1 + \frac{1}{\textsf{x}} \right) \left( 1 + \frac{1}{\textsf{y}} \right)$ is

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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3 votes

1 answer

156

CAT 2020 Set-2 | Question: 57
The value of $\log_{a} \left( \frac {a}{b} \right) + \log_{b} \left( \frac{b}{a} \right),$ for $ 1 < a \leq b$ cannot be equal to $ – 0.5$ $1$ $0$ $ – 1$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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157

CAT 2020 Set-2 | Question: 58
In how many ways can a pair of integers $\textsf{(x , a)}$ be chosen such that $x^{2} – 2 |x| + |a-2| = 0 ?$ $4$ $5$ $6$ $7$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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158

CAT 2020 Set-2 | Question: 59
Students in a college have to choose at least two subjects from chemistry, mathematics, and physics. The number of students choosing all three subjects is $18,$ choosing mathematics as one of their subjects is $23$ and choosing physics as one of their ... smallest possible number of students who could choose chemistry as one of their subjects is $20$ $22$ $19$ $21$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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2 votes

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159

CAT 2020 Set-2 | Question: 60
For real $\textsf{x}$ , the maximum possible value of $ \frac{x}{\sqrt{1+x^{4}}}$ is $ \frac{1}{\sqrt{3}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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160

CAT 2020 Set-2 | Question: 67
If $\textsf{x}$ and $\textsf{y}$ are non-negative integers such that $\textsf{x+9=z, y+1=z}$ and $\textsf{x+y<z+5},$ then the maximum possible value of $\textsf{2x+y}$ equals

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

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