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Recent questions and answers

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1

CAT2020-1: 54
On a rectangular metal sheet of area $135$ sq in, a circle is painted such that the circle touches two opposite sides. If the area of the sheet left unpainted is two$-$ ... $3\sqrt{\pi }\left ( 5+\frac{12}{\pi} \right )$ $4\sqrt{\pi }\left ( 3+\frac{9}{\pi} \right )$

Anam_ALP answered in Quantitative Aptitude 10 hours ago

4.9k points

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1 answer

2

CAT2020-1: 53
An alloy is prepared by mixing three metals $A, B$ and $C$ in the proportion $3:4:7$ by volume. Weights of the same volume of the metals $A, B$ and $C$ are in the ratio $5:2:6$. In $130$ kg of the alloy, the weight, in kg, of the metal $C$ is $70$ $96$ $48$ $84$

Anam_ALP answered in Quantitative Aptitude 11 hours ago

4.9k points

33 views

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1 answer

3

CAT2020-1: 52
Veeru invested Rs $10000$ at $5\%$ simple annual interest, and exactly after two years, Joy invested Rs $8000$ at $10\%$ simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

Anam_ALP answered in Quantitative Aptitude 11 hours ago

4.9k points

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4

CAT2020-1: 51
How many $3-$digit numbers are there, for which the product of their digits is more than $2$ but less than $7$?

Anam_ALP answered in Quantitative Aptitude 11 hours ago

4.9k points

25 views

2 votes

1 answer

5

CAT2020-3: 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 $439$ $399$ $357$ $417$

Hira Thakur answered in Quantitative Aptitude Nov 9

4k points

44 views

2 votes

2 answers

6

CAT2020-3: 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

Hira Thakur answered in Quantitative Aptitude Nov 9

4k points

52 views

1 vote

1 answer

7

CAT2020-1: 68
If $f\left ( 5+x \right )= f\left ( 5-x \right )$ for every real $x,$ and $f\left ( x \right )=0$ has four distinct real roots, then the sum of these roots is $0$ $40$ $10$ $20$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

35 views

3 votes

1 answer

8

CAT2020-1: 73
Let $A, B$ and $C$ be three positive integers such that the sum of $A$ and the mean of $B$ and $C$ is $5$. In addition, the sum of $B$ and the mean of $A$ and $C$ is $7$. Then the sum of $A$ and $B$ is $6$ $5$ $7$ $4$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

44 views

1 vote

1 answer

9

CAT2020-1: 75
The number of distinct real roots of the equation $\left ( x+\frac{1}{x}\right )^{2}-3\left ( x+\frac{1}{x} \right )+2= 0$ equals

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

38 views

1 vote

1 answer

10

CAT2020-1: 67
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$? $\frac{x^{7}}{x^{2\sqrt{3}}}$ $\frac{x^{7}}{x^{4\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x\frac{4}{\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x^{2\sqrt{3}}}$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

34 views

1 vote

1 answer

11

CAT2020-1: 58
If $y$ is a negative number such that $2^{y^{2}\log _{2}3}=5^{\log_{2}3}$, then $y$ equals $\log _{2}\left ( \frac{1}{3} \right )$ $-\log _{2}\left ( \frac{1}{3} \right )$ $\log _{2}\left ( \frac{1}{5} \right )$ $-\log _{2}\left ( \frac{1}{5} \right )$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

44 views

2 votes

1 answer

12

CAT2020-1: 55
If $\log_4 5=\left ( \log _{4}y \right )\left ( \log _{6}\sqrt{5} \right )$, then $y$ equals

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

41 views

1 vote

1 answer

13

CAT2020-3: 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

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

41 views

2 votes

1 answer

14

CAT2020-3: 73
$\dfrac{2 \times 4 \times 8 \times 16} {(\log_{2} 4)^{2} (\log_{4} 8)^{3} (\log_{8} 16)^{4}}$ equals

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

33 views

2 votes

1 answer

15

CAT2020-3: 71
How many of the integers $1,2, \dots, 120,$ are divisible by none of $2,5$ and $7 ?$ $40$ $42$ $43$ $41$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

39 views

1 vote

1 answer

16

CAT2020-3: 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 $7$ $8$ $5$ $6$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

40 views

1 vote

1 answer

17

CAT2020-3: 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 $?$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

32 views

1 vote

1 answer

18

CAT2020-3: 58
If $ f(x+y) = f(x) f(y) $ and $ f(5) = 4,$ then $ f(10) – f(-10) $ is equal to $0$ $15.9375$ $3$ $14.0625$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

45 views

1 vote

1 answer

19

CAT2020-3: 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 $

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

30 views

1 vote

1 answer

20

CAT2020-3: 54
Let $\text{k}$ be a constant. The equations $\text{kx + y} = 3$ and $\text{4x + ky} = 4$ have a unique solution if and only if $|\text{k}| \neq 2$ $|\text{k}| = 2$ $\text{k} \neq 2$ $\text{k} = 2$

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

39 views

2 votes

1 answer

21

CAT2020-3: 51
If $\log_{a} 30 = A, \log_{a} (5/3) = – B $ and $\log_{2} a = 1/3,$ then $\log_{3}a $ equals $ \frac{2}{A + B} – 3 $ $ \frac{A + B - 3}{2} $ $ \frac{2}{A + B – 3} $ $ \frac{A + B}{2} – 3 $

Anam_ALP answered in Quantitative Aptitude Oct 31

4.9k points

45 views

1 vote

1 answer

22

CAT1995-178
Machine M1 as well as Machine M2 can independently produce either Product P or Product Q. The times taken by machines M1 and M2 (in minutes) to produce one unit of product P and Q are given in the table below: (Each machine works 8 hours per day). PRODUCT M1 M2 ... of each with 3 minutes idle 64 of each with 12 minutes idle 53 of each with 10 minutes idle 71 of each with 9 minutes idle

Sai Pavan Kavya answered in Quantitative Aptitude Oct 30

by Sai Pavan Kavya

18 points

1.8k views

1 vote

1 answer

23

CAT2020-2: 73
Let $\text{C}1$ and $\text{C}2$ be concentric circles such that the diameter of $\text{C}1$ is $2 \; \text{cm}$ longer than that of $\text{C}2.$ If a chord of $\text{C}1$ has length $6 \; \text{cm}$ and is a tangent to $\text{C}2,$ then the diameter, in $\text{cm},$ of $\text{C}1$ is

Anam_ALP answered in Quantitative Aptitude Oct 30

4.9k points

43 views

1 vote

1 answer

24

CAT2020-2: 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 $?$ $₹580$ $₹570$ $₹560$ $₹590$

Anam_ALP answered in Quantitative Aptitude Oct 30

4.9k points

38 views

1 vote

1 answer

25

CAT2020-2: 70
Let $\text{C}$ be a circle of radius $5 \; \text{meters}$ having center at $\text{O}.$ Let $\text{PQ}$ be a chord of $\text{C}$ that passes through points $\text{A}$ and $\text{B}$ where $\text{A}$ is located $4 \; \text{meters}$ north of $\text{O}$ and $\text{B}$ ... $\text{O}.$ Then, the length of $\text{PQ}$, in meters, is nearest to $7.2$ $7.8$ $6.6$ $8.8$

Anam_ALP answered in Quantitative Aptitude Oct 30

4.9k points

45 views

1 vote

1 answer

26

CAT2020-2: 69
The distance from $\text{B}$ to $\text{C}$ is thrice that from $\text{A}$ to $\text{B}.$ Two trains travel from $\text{A}$ to $\text{C}$ via $\text{B}.$ The speed of train $2$ is double that of train $1$ while traveling from $\text{A}$ to $\text{B}$ and their speeds are ... by train $1$ to that taken by train $2$ in traveling from $\text{A}$ to $\text{C}$ is $1:4$ $7:5$ $5:7$ $4:1$

Anam_ALP answered in Quantitative Aptitude Oct 30

4.9k points

33 views

1 vote

1 answer

27

CAT2020-2: 68
$\text{A}$ and $\text{B}$ are two points on a straight line. Ram runs from $\text{A}$ to $\text{B}$ while Rahim runs from $\text{B}$ to $\text{A}.$ After crossing each other, Ram and Rahim reach their destinations in one minute and four minutes, respectively. If they start at the same time, then the ratio of Ram’s speed to Rahim’s speed is $2$ $\sqrt{2}$ $2\sqrt{2}$ $\frac{1}{2}$

Anam_ALP answered in Quantitative Aptitude Oct 29

4.9k points

89 views

2 votes

1 answer

28

CAT2020-2: 76
In a group of $10$ students, the mean of the lowest $9$ scores is $42$ while the mean of the highest $9$ scores is $47.$ For the entire group of $10$ students, the maximum possible mean exceeds the minimum possible mean by $4$ $3$ $5$ $6$

Anam_ALP answered in Quantitative Aptitude Oct 29

4.9k points

35 views

2 votes

1 answer

29

CAT2020-2: 72
Let $f(x) = x^{2} + ax + b $ and $g(x) = f(x+1) – f(x-1).$ If $ f(x) \geq 0 $ for all real $x,$ and $ g(20) = 72,$ then the smallest possible value of $b$ is $1$ $16$ $0$ $4$

Anam_ALP answered in Quantitative Aptitude Oct 29

4.9k points

31 views

3 votes

1 answer

30

CAT2020-2: 71
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$ $3$ $5$ $4$

Anam_ALP answered in Quantitative Aptitude Oct 29

4.9k points

37 views

2 votes

1 answer

31

CAT2020-2: 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

Anam_ALP answered in Quantitative Aptitude Oct 29

4.9k points

22 views

1 vote

1 answer

32

CAT2020-2: 65
How many $4$-digit numbers, each greater than $1000$ and each having all four digits distinct, are there with $7$ coming before $3$

Anam_ALP answered in Quantitative Aptitude Oct 29

4.9k points

36 views

1 vote

1 answer

33

CAT2020-2: 64
Two circular tracks $\text{T}1$ and $\text{T}2$ of radii $100 \; \text{m}$ and $20 \; \text{m},$ respectively touch at a point $\text{A}.$ Starting from $\text{A}$ at the same time, Ram and Rahim are walking on track $\text{T}1$ ... $4$ $3$ $2$ $5$

Anam_ALP answered in Quantitative Aptitude Oct 28

4.9k points

34 views

2 votes

1 answer

34

CAT2020-2: 62
A sum of money is split among Amal, Sunil and Mita so that the ratio of the shares of Amal and Sunil is $3:2,$ while the ratio of the shares of Sunil and Mita is $4:5.$ If the difference between the largest and the smallest of these three shares is $\text{Rs.} 400,$ then Sunil’s share, in rupees, is

Anam_ALP answered in Quantitative Aptitude Oct 28

4.9k points

35 views

2 votes

1 answer

35

CAT2020-2: 60
For real $\textsf{x}$ , the maximum possible value of $ \frac{x}{\sqrt{1+x^{4}}}$ is $ \frac{1}{\sqrt{3}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$

Anam_ALP answered in Quantitative Aptitude Oct 28

4.9k points

30 views

2 votes

1 answer

36

CAT2020-2: 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$

Anam_ALP answered in Quantitative Aptitude Oct 28

4.9k points

48 views

2 votes

1 answer

37

CAT2020-2: 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

Anam_ALP answered in Quantitative Aptitude Oct 27

4.9k points

42 views

2 votes

1 answer

38

CAT2020-2: 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$

Anam_ALP answered in Quantitative Aptitude Oct 27

4.9k points

55 views

1 vote

1 answer

39

CAT2020-2: 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 $500$ $475$ $550$ $450$

Anam_ALP answered in Quantitative Aptitude Oct 27

4.9k points

24 views

1 vote

1 answer

40

CAT2020-2: 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 $\text{sq cm},$ ... sides of the rectangle are in the ratio $1:3,$ then the length, in cm, of the longer side of the rectangle, is $24$ $27$ $21$ $18$

Anam_ALP answered in Quantitative Aptitude Oct 27

4.9k points

71 views

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