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CAT 2022 Set-3 | Quantitative Aptitude | Question: 2
If $c=\dfrac{16 x}{y}+\dfrac{49 y}{x}$ for some non-zero real numbers $x$ and $y,$ then $c$ cannot take the value $-60$ $-50$ $60$ $-70$

admin asked in Quantitative Aptitude Mar 3

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2

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

by soujanyareddy13

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402 views

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3

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

by soujanyareddy13

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4

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

by soujanyareddy13

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2 votes

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5

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

by soujanyareddy13

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2 votes

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6

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

by soujanyareddy13

2.7k points

452 views

3 votes

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7

CAT 2020 Set-2 | Question: 71
The number of integers that satisfy the equality $\left( x^{2} – 5x + 7 \right)^{x+1} = 1$ is $2$ $3$ $5$ $4$

soujanyareddy13 asked in Quantitative Aptitude Sep 17, 2021

by soujanyareddy13

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445 views

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8

CAT 2020 Set-1 | Question: 57
The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is infinite $1$ $0$ $2$

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

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9

CAT 2020 Set-1 | Question: 59
How many distinct positive integer-valued solutions exist to the equation $\left ( x^{2}-7x+11 \right )^{(x^{2}-13x+42)} =1$? $6$ $8$ $2$ $4$

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

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430 views

2 votes

1 answer

10

CAT 2020 Set-1 | Question: 67
If $x=\left ( 4096 \right )^{7+4\sqrt{3}}$, then which of the following equals $64$? $\frac{x^{7}}{x^{2\sqrt{3}}}$ $\frac{x^{7}}{x^{4\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x\frac{4}{\sqrt{3}}}$ $\frac{x\frac{7}{2}}{x^{2\sqrt{3}}}$

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

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11

CAT 2020 Set-1 | Question: 69
If $a, b$ and $c$ are positive integers such that $ab=432, bc=96$ and $c<9,$ then the smallest possible value of $a+b+c$ is $56$ $59$ $49$ $46$

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

2.7k points

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12

CAT 2020 Set-1 | Question: 72
A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving ... fashion. His total stock exhausts after he takes care of $5$ children. How many toffees were there in his stock initially?

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

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13

CAT 2020 Set-1 | Question: 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

soujanyareddy13 asked in Quantitative Aptitude Sep 16, 2021

by soujanyareddy13

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507 views

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14

NIELIT 2016 MAR Scientist D: 71
A certain number when added to $50\%$ of itself is $27$. What is the number? $7$ $9$ $11$ $18$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 3, 2020

by Lakshman Bhaiya

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15

NIELIT 2016 MAR Scientist D: 70
Twelve less than $4$ times a number is $20$. What is the number? $2$ $4$ $6$ $8$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 3, 2020

by Lakshman Bhaiya

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549 views

1 vote

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16

NIELIT 2016 MAR Scientist D: 69
The sum of a number and its double is $69$. What is the number? $46.6$ $34.5$ $23$ $20$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 3, 2020

by Lakshman Bhaiya

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17

NIELIT 2019 Feb Scientist D - Section D: 3
A school has $378$ girls and $675$ boys. All the students divided into strictly boys and strictly girls students sections. All the sections in the school has same number of students. What is the number of sections in the school? $27$ $36$ $39$ $23$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 3, 2020

by Lakshman Bhaiya

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18

NIELIT 2019 Feb Scientist D - Section D: 26
A dog at point $A$ goes in pursuit of a fox $30$ $m$ away. The dog makes $2$ $m$ and the fox, $1$ m long leaps. If the dog makes two leaps to the fox’s three, at what distance from $A$ will the dog catch up with the fox ? $100$ $m$ $110$ $m$ $105$ $m$ $120$ $m$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 3, 2020

by Lakshman Bhaiya

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19

NIELIT 2019 Feb Scientist D - Section D: 27
If $5$ spiders can catch $5$ files in $5$ minutes. How many files can $100$ spiders catch in $100$ minutes : $100$ $1000$ $500$ $2000$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 3, 2020

by Lakshman Bhaiya

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20

NIELIT 2016 MAR Scientist C - Section A: 12
The expression $(11.98\times 11.98 + 11.98 \times x +0.02 \times 0.02)$ will be a perfect square for $x$ equal to: $2.02$ $0.17$ $0.04$ $1.4$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 2, 2020

by Lakshman Bhaiya

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21

NIELIT 2016 MAR Scientist C - Section A: 15
The value of $\large\frac{(0.96)^3-(0.1)^3}{(0.96)^2+0.096+(0.1)^2}$ is : $0.86$ $0.95$ $0.97$ $1.06$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 2, 2020

by Lakshman Bhaiya

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868 views

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22

NIELIT 2019 Feb Scientist C - Section D: 15
The simplified form of $\left[ \left ( \left( \dfrac{a+1}{a-1}\right)^2+3 \right)\div \left( \left( \dfrac{a-1}{a+1}\right)^2+3\right) \right] \div \left [\left( \dfrac{a^{3}+1}{a^{3}-1}\right)-\dfrac{2a}{a-1} \right]$ is: $a-1$ $1-a$ $-1$ $1$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

by Lakshman Bhaiya

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553 views

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2 answers

23

NIELIT 2019 Feb Scientist C - Section D: 23
Rs.$6500$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $Rs.30$ less. Find the original number of persons. $50$ $60$ $45$ $55$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

by Lakshman Bhaiya

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24

NIELIT 2019 Feb Scientist C - Section D: 30
A charitable trust donates $28$ different books of Maths, $16$ different books of science and $12$ different books of social science to poor students. Each student is given maximum number of books of only one subject of their interest and each student got equal number of books. Find the total number of students who got books. $14$ $10$ $12$ $15$

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

by Lakshman Bhaiya

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812 views

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25

NIELIT 2019 Feb Scientist C - Section C: 3
The factors of $(x^{2}+4y^{2}+4y-4xy-2x-8)$ are: $(x-2y-4)(x-2y+2)$ $(x-y+2)(x-4y-4)$ $(x+2y-4)(x+2y+2)$ None of these

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

by Lakshman Bhaiya

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616 views

1 vote

2 answers

26

NIELIT 2019 Feb Scientist C - Section C: 19
If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals: $abc$ $\dfrac{1}{abc}$ $1$ None

Lakshman Bhaiya asked in Quantitative Aptitude Apr 1, 2020

by Lakshman Bhaiya

13.6k points

639 views

1 vote

1 answer

27

CAT 2019 Set-2 | Question: 86
What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$

go_editor asked in Quantitative Aptitude Mar 20, 2020

13.7k points

906 views

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28

CAT 2019 Set-2 | Question: 97
If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______

go_editor asked in Quantitative Aptitude Mar 20, 2020

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3 votes

1 answer

29

CAT 2018 Set-1 | Question: 69
Given that $x^{2018}y^{2017}=1/2$ and $x^{2016}y^{2019}=8$, the value of $x^2+y^3$ is $35/4$ $37/4$ $31/4$ $33/4$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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614 views

2 votes

1 answer

30

CAT 2018 Set-1 | Question: 77
If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ? $1/4$ $0$ $1/2$ $-1/4$

go_editor asked in Quantitative Aptitude Mar 20, 2020

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31

CAT 2017 Set-2 | Question: 94
How many different pairs $(a,b)$ of positive integers are there such that $a\leq b$ and $1/a+1/b=1/9$ None of these $2$ $0$ $1$

go_editor asked in Quantitative Aptitude Mar 16, 2020

13.7k points

424 views

2 votes

2 answers

32

CAT 2017 Set-2 | Question: 91
If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is $3/2$ $2/5$ $3/4$ $4/9$

go_editor asked in Quantitative Aptitude Mar 16, 2020

13.7k points

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33

CAT 2017 Set-1 | Question: 90
If $9^{2x-1}-81^{x-1}= 1944$ then $x$ is $3$ $9/4$ $4/9$ $1/3$

go_editor asked in Quantitative Aptitude Mar 13, 2020

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452 views

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34

CAT 2017 Set-1 | Question: 88
If $x+1= x^{2}$ and $x> 0$, then $2x^{4}$ is $6+4\sqrt{5}$ $3+5\sqrt{5}$ $5+3\sqrt{5}$ $7+3\sqrt{5}$

go_editor asked in Quantitative Aptitude Mar 13, 2020

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35

CAT 2017 Set-1 | Question: 94
If $a, b, c$ and $d$ are integers such that $a+b+c+d=30$ , then the minimum possible value of $( a-b )^{2}+( a-c )^{2}+( a-d)^{2}$ is $1$ $2$ $5$ $6$

go_editor asked in Quantitative Aptitude Mar 13, 2020

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36

CAT 2016 | Question: 100
If three positive real numbers $x,y,z$ satisfy $y–x=z–y$ and $xyz = 4$, then what is the minimum possible value of $y$? $2^{(1/3)}$ $2^{(2/3)}$ $2^{(1/4)}$ $2^{(3/4)}$

go_editor asked in Quantitative Aptitude Mar 11, 2020

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37

CAT 2015 | Question: 92
Let $x<0,\:0<y<1,\:z>1$. Which of the following may be false? $\left (x ^{2} -z^{2}\right )$ has to be positive. $yz$ can be less than one. $xy$ can never be zero. $\left (y ^{2} -z^{2}\right )$ is always negative.

go_editor asked in Quantitative Aptitude Mar 9, 2020

13.7k points

391 views

2 votes

1 answer

38

CAT 2019 Set-1 | Question: 83
If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$

go_editor asked in Quantitative Aptitude Mar 8, 2020

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39

CAT 2011 | Question: 51
Given $\text{a}$ and $\text{b = a-b; a}$ and $\text{b}$ but $\text{c=a+c-b; a}$ or $\text{b=b-a; a}$ but not $\text{b= a+b}$; find $1$ or $(2$ but not $(3$ or $(4$ and $5$ but $(6$ but not $(7$ and $(8$ or $9) ) ) ) ) ).$ $9$ $-8$ $-11$ $17$

Krithiga2101 asked in Logical Reasoning Mar 7, 2020

by Krithiga2101

298 points

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40

CAT 2011 | Question: 53
Consider the following operators defined below $x@y$: gives the positive difference of $x$ and $y.$ $x\$y$: gives the sum of squares of $x$ and $y.$ $x₤y$: gives the positive difference of the squares of $x$ and $y.$ $x\&y$:gives the product of $ ... $ will be equal to $x₤y$ $x\$y$ $(x₤y)(x@y)$ Cannot be determined

Krithiga2101 asked in Logical Reasoning Mar 7, 2020

by Krithiga2101

298 points

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