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CAT 2023 Set-3 | Quantitative Aptitude | Question: 17
Q. 17)Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the ... $\cos 15^{\circ}$2 \cos 15^{\circ}$2 \sin 15^{\circ}$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 18
Q. 18)A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is$1: 1$\sqrt{5}: 1$\sqrt{2}: 1$2: 1$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 19
Q. 19)In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 20
Q. 20)Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is14900150001479814602
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 21
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 22
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 4
Q. 4)For a real number $x$, if $\frac{1}{2}, \frac{\log _{3}\left(2^{x}-9\right)}{\log _{3} 4}$ ... $\log _{4}\left(\frac{7}{2}\right)$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 5
Q. 5)A quadratic equation $x^{2}+b x+c=0$ has two real roots. If the difference between the reciprocals of the roots is $\frac{1}{3}$, and the sum of the ... the roots is $\frac{5}{9}$, then the largest possible value of $(b+c)$ is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 6
Q. 6)The sum of the first two natural numbers, each having 15 factors (including 1 and the number itself), is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 7
Q. 7)Let $n$ be any natural number such that $5^{n-1}
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 8
Q. 8)A boat takes 2 hours to travel downstream a river from port $A$ to port $B$, and 3 hours to return to port A. Another boat takes a total of 6 hours to travel from port $B$ ... 3(\sqrt{5}-1)$3(3+\sqrt{5})$3(3-\sqrt{5})$12(\sqrt{5}-2)$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 9
Q. 9)Anil mixes cocoa with sugar in the ratio $3: 2$ to prepare mixture $A$, and coffee with sugar in the ratio $7: 3$ to prepare mixture $B$. ... amount of milk to make a drink, then the percentage of sugar in this drink will be16241721
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 10
Q. 10)Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working ... then the number of days she would have taken to finish the job, cannot be16211720
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 11
Q. 11)The population of a town in 2020 was 100000 . The population decreased by $y \%$ from the year 2020 to 2021, and increased by $x \%$ ... and $y$ is 10 , then the lowest possible population of the town in 2021 was74000750007300072000
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 12
Q. 12)There are three persons $A, B$ and $C$ in a room. If a person $D$ ... $\mathrm{D}$, then the value of $x$ is1.50.512
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 13
Q. 13)A merchant purchases a cloth at a rate of Rs. 100 per meter and receives $5 \mathrm{~cm}$ length of cloth free for every $100 \mathrm{~cm}$ length of cloth purchased ... $16 \%$4.2 \%$15.5 \%$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 14
Q. 14)Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only $60 \%$ ... Then, the number of days required by the faster worker to complete the job working alone is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 15
Q. 15)The number of coins collected per week by two coin-collectors $A$ and $B$ are in the ratio $3: 4$. If the total number of coins collected by $A$ ... of 24 , then the minimum possible number of coins collected by $A$ in one week is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 16
Q. 16)A fruit seller has a stock of mangoes, bananas and apples with at least one fruit of each type. At the beginning of a day, the number of mangoes ... smallest possible total number of fruits in the stock at the beginning of the day is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 17
Q. 17)Let $\triangle A B C$ be an isosceles triangle such that $A B$ and $A C$ are of equal length. $A D$ is the altitude from $A$ on $B C$ and $B E$ is the ... $\cos 15^{\circ}$2 \cos 15^{\circ}$2 \sin 15^{\circ}$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 18
Q. 18)A rectangle with the largest possible area is drawn inside a semicircle of radius $2 \mathrm{~cm}$. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is$1: 1$\sqrt{5}: 1$\sqrt{2}: 1$2: 1$
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 19
Q. 19)In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 20
Q. 20)Let $a_{n}=46+8 n$ and $b_{n}=98+4 n$ be two sequences for natural numbers $n \leq 100$. Then, the sum of all terms common to both the sequences is14900150001479814602
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 21
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CAT 2023 Set-3 | Quantitative Aptitude | Question: 22
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 1
For any natural numbers $\mathrm{m}, \mathrm{n}$, and $\mathrm{k}$, such that $\mathrm{k}$ divides both $m+2 n$ and $3 m+4 n \mathrm{k}$ must be a common divisor of$m$ and $n$2 m$ and $3 n$2 m$ and $n$m$ and $2 n$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 2
Any non-zero real numbers $\mathrm{x}$, $\mathrm{y}$ such that $y \neq 3$ and $\frac{x}{y}<\frac{x+3}{y-3}$, will satisfy the condition$\frac{x}{y}<\frac{y}{x}$If $y>10$, then $-x>y$If $x<0$, then $-xIf $y<0$, then $-x
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 3
The sum of all possible values of $x$ satisfying the equation $2^{4 x^{2}}-2^{2 x^{2}+x+16}+2^{2 x+30}=0$, is$\frac{5}{2}$\frac{1}{2}$3$\frac{3}{2}$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 4
Let $\mathrm{a}, \mathrm{b}, \mathrm{m}$ and $\mathrm{n}$ be natural numbers such that $a>1$ and $b>1$. If $a^{m} b^{n}=144^{145}$, then the largest possible value of $n-m$ is$579$289$580$290$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 5
The number of positive integers less than $50$, having exactly two distinct factors other than $1$ and itself, is
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 6
Let $k$ be the largest integer such that the equation $(x-1)^{2}+2 k x+11=0$ has no real roots. If $y$ is a positive real number, then the least possible value of $\frac{k}{4 y}+9 y$ is
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 7
For some positive real number $x$, if $\log _{\sqrt{3}}(x)+\frac{\log _{x}(25)}{\log _{x}(0.008)}=\frac{16}{3}$, then the value of $\log _{3}\left(3 x^{2}\right)$ is
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 8
Pipes $\mathrm{A}$ and $\mathrm{C}$ are fill pipes while Pipe $\mathrm{B}$ is a drain pipe of a tank. Pipe $\mathrm{B}$ empties the full tank in one hour less ... $ to fill the empty tank is$75$120$60$90$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 9
Ravi is driving at a speed of $40 \mathrm{~km} / \mathrm{h}$ on a road. Vijay is $54$ meters behind Ravi and driving in the same direction as Ravi. Ashok is driving ... $64.4$61.6$58.8$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 10
In a company, $20 \%$ of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary ... $4: 5$5: 4$5: 6$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 11
Minu purchases a pair of sunglasses at Rs. $1000$ and sells to Kanu at $20 \%$ profit. Then, Kanu sells it back to Minu at $20 \%$ loss. Finally, Minu sells the same ... $35.42 \%$52 \%$31.25 \%$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 12
The price of a precious stone is directly proportional to the square of its weight. Sita has a precious stone weighing $18$ units. If she breaks it into ... $1296000$1944000$972000$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 13
Anil borrows Rs $2$ lakhs at an interest rate of $8 \%$ per annum, compounded half-yearly. He repays Rs $10320$ at the end of the first year and ... $40991$51311$45311$
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 14
A container has $40$ liters of milk. Then, $4$ liters are removed from the container and replaced with $4$ ... after which the volume of milk in the container becomes less than that of water, is
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CAT 2023 Set-2 | Quantitative Aptitude | Question: 15
Jayant bought a certain number of white shirts at the rate of Rs $1000$ per piece and a certain number of blue shirts at the rate of Rs $1125$ per ... of shirts, then the maximum possible total number of shirts that he could have bought is
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