Recent questions tagged algebra

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1

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 $

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 $

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 101 views

1 vote

1 answer

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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

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

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 150 views

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

How many pairs $(a,b)$ of positive integers are there such that $a \leq b$ and $ab = 4^{2017} \; ?$ $2017$ $2019$ $2020$ $2018$

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 33 views

2 votes

1 answer

4

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

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

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 129 views

2 votes

1 answer

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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}}$ $1$ $\frac{1}{\sqrt{2}}$ $\frac{1}{2}$

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

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 114 views

3 votes

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

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

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 130 views

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1 answer

7

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

The number of real$-$valued of the equation $2^{x}+2^{-x}=2-(x-2)^{2}$ is infinite $1$ $0$ $2$

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 133 views

1 vote

1 answer

8

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

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

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 109 views

2 votes

1 answer

9

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

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

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 86 views

1 vote

1 answer

10

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 $56$ $59$ $49$ $46$

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 $56$ $59$ $49$ $46$

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 108 views

1 vote

1 answer

11

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?

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 away in this fashion. His total stock exhausts after he takes care of $5$ children. How many toffees were there in his stock initially?

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 113 views

1 vote

1 answer

12

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

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

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 102 views

1 vote

1 answer

13

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

A certain number when added to $50\%$ of itself is $27$. What is the number? $7$ $9$ $11$ $18$

asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 198 views

0 votes

1 answer

14

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

Twelve less than $4$ times a number is $20$. What is the number? $2$ $4$ $6$ $8$

asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 265 views

1 vote

1 answer

15

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

The sum of a number and its double is $69$. What is the number? $46.6$ $34.5$ $23$ $20$

asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 207 views

0 votes

1 answer

16

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? $27$ $36$ $39$ $23$

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? $27$ $36$ $39$ $23$

asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 302 views

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1 answer

17

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 ? $100$ $m$ $110$ $m$ $105$ $m$ $120$ $m$

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 ? $100$ $m$ $110$ $m$ $105$ $m$ $120$ $m$

asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 318 views

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18

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 : $100$ $1000$ $500$ $2000$

If $5$ spiders can catch $5$ files in $5$ minutes. How many files can $100$ spiders catch in $100$ minutes : $100$ $1000$ $500$ $2000$

asked Apr 3, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 210 views

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19

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: $2.02$ $0.17$ $0.04$ $1.4$

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: $2.02$ $0.17$ $0.04$ $1.4$

asked Apr 2, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 112 views

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1 answer

20

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 : $0.86$ $0.95$ $0.97$ $1.06$

The value of $\large\frac{(0.96)^3-(0.1)^3}{(0.96)^2+0.096+(0.1)^2}$ is : $0.86$ $0.95$ $0.97$ $1.06$

asked Apr 2, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 304 views

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21

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: $a-1$ $1-a$ $-1$ $1$

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: $a-1$ $1-a$ $-1$ $1$

asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 158 views

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1 answer

22

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

$₹6500/-$ were divided among a certain number of persons. If there had been $15$ more persons, each would have got $₹30/-$ less. Find the original number of persons. $50$ $60$ $45$ $55$

asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 323 views

0 votes

1 answer

23

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. $14$ $10$ $12$ $15$

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. $14$ $10$ $12$ $15$

asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 348 views

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1 answer

24

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

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

asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 251 views

1 vote

2 answers

25

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

If $a^{x}=b, b^{y}=c$ and $c^{z}=a$, then $xyz$ equals: $abc$ $\dfrac{1}{abc}$ $1$ None

asked Apr 1, 2020 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 284 views

1 vote

1 answer

26

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? $8$ $12$ $16$ $6$

What is the largest positive integer $n$ such that $\frac{n^{2}+7n+12}{n^{2}-n-12}$ is also a positive integer? $8$ $12$ $16$ $6$

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 356 views

1 vote

1 answer

27

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

If $5^{x}-3^{y}=13438$ and $5^{x-1}+3^{y+1}=9686$, then $x+y$ equals _______

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 261 views

2 votes

1 answer

28

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 $35/4$ $37/4$ $31/4$ $33/4$

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

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 216 views

2 votes

1 answer

29

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

If $u^2+(u-2v-1)^2=-4v(u+v)$, then what is the value of $u+3v$ ? $1/4$ $0$ $1/2$ $-1/4$

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 154 views

1 vote

1 answer

30

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 $2$ $0$ $1$

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 $2$ $0$ $1$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 146 views

1 vote

1 answer

31

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 $3/2$ $2/5$ $3/4$ $4/9$

If $9^{\left ( x-1/2 \right )}-2^{\left ( 2x-2 \right )}=4^{x}-3^{\left (2x-3 \right )}$, then $x$ is $3/2$ $2/5$ $3/4$ $4/9$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 150 views

1 vote

1 answer

32

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

If $9^{2x-1}-81^{x-1}= 1944$ then $x$ is $3$ $9/4$ $4/9$ $1/3$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 162 views

1 vote

1 answer

33

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

If $x+1= x^{2}$ and $x> 0$, then $2x^{4}$ is $6+4\sqrt{5}$ $3+5\sqrt{5}$ $5+3\sqrt{5}$ $7+3\sqrt{5}$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 191 views

1 vote

1 answer

34

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 $1$ $2$ $5$ $6$

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 $1$ $2$ $5$ $6$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 136 views

1 vote

1 answer

35

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 $y$? $2^{(1/3)}$ $2^{(2/3)}$ $2^{(1/4)}$ $2^{(3/4)}$

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

asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 152 views

0 votes

1 answer

36

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.

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.

asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 144 views

2 votes

1 answer

37

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 $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$

If $(5.55)^{x}=(0.555)^{y}=1000$, then the value of $\frac{1}{x}-\frac{1}{y}$ is $3$ $1$ $\frac{1}{3}$ $\frac{2}{3}$

asked Mar 8, 2020 in Quantitative Aptitude go_editor 13.3k points 209 views

0 votes

0 answers

38

CAT 2011 | Question: 53
Consider the following operators defined below [email protected]$: 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 $x₤y$ $x\$y$ $(x₤y)([email protected])$ Cannot be determined

Consider the following operators defined below [email protected]$: 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 $x$ and $ ... $ will be equal to $x₤y$ $x\$y$ $(x₤y)([email protected])$ Cannot be determined

asked Mar 7, 2020 in Logical Reasoning Krithiga2101 262 points 66 views

0 votes

0 answers

39

CAT 2011 | Question: 52
Consider the following operators defined below [email protected]$: 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 $x$ and $ ... $, then find $(x\$y)+(x₤y)$. $2x^2$ $2y^2$ $2(x^2+y^2)$ Cannot be determined

Consider the following operators defined below [email protected]$: 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 $x$ and $y.$ Also, $x,y\:\in ... $, then find $(x\$y)+(x₤y)$. $2x^2$ $2y^2$ $2(x^2+y^2)$ Cannot be determined

asked Mar 7, 2020 in Logical Reasoning Krithiga2101 262 points 92 views

0 votes

0 answers

40

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

Given $a$ and $b = a-b$; $a$ and $b$ but $c=a+c-b$; $a$ or $b=b-a$; $a$ but not $b= a+b$; find $1$ or $(2$ but not $(3$ or $(4$ and $5$ but $(6$ but not $(7$ and $(8$ or $9) ) ) ) ) ).$ $9$ $-8$ $-11$ $17$

asked Mar 7, 2020 in Logical Reasoning Krithiga2101 262 points 117 views

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