Recent questions tagged functions

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CAT 2004 | Question: 62
Answer the questions on the basis of the information given below: $f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matrix}\right.$ $f_{2}(x) = f_{1}(-x) \;\; \text{for all} \; x $ ... $f_2(-x) = f_4(x) \: \text{for all }\;x$ $f_1(x) + f_3(x) = 0 \: \text{for all }\;x$

Answer the questions on the basis of the information given below: $f_{1}(x) = \left\{\begin{matrix} x & 0 \leq x \leq 1 \\ 1 & x \geq 1 \\ 0 & \text{otherwise} \end{matrix}\right.$ $f_{2}(x) = f_{1}(-x) \;\; \text{for all} \; x $ ... $f_2(-x) = f_4(x) \: \text{for all }\;x$ $f_1(x) + f_3(x) = 0 \: \text{for all }\;x$

asked Mar 30 in Quantitative Aptitude Lakshman Patel RJIT 10.7k points 33 views

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CAT 2021 Set-3 | Quantitative Aptitude | Question: 12
If $f(x) = x^{2} – 7x$ and $g(x) = x + 3,$ then the minimum value of $f(g(x)) – 3x$ is $ -16$ $ -15$ $ -20$ $ -12$

If $f(x) = x^{2} – 7x$ and $g(x) = x + 3,$ then the minimum value of $f(g(x)) – 3x$ is $ -16$ $ -15$ $ -20$ $ -12$

asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 59 views

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CAT 2021 Set-2 | Quantitative Aptitude | Question: 15
For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is $ \left(\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{8}{9} \right)$ $ \left[\frac{4}{9}, \frac{8}{9} \right]$

For all real values of $x,$ the range of the function $f(x) = \dfrac{x^{2} + 2x + 4}{2x^{2} + 4x + 9}$ is $ \left(\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{1}{2} \right)$ $ \left[\frac{3}{7}, \frac{8}{9} \right)$ $ \left[\frac{4}{9}, \frac{8}{9} \right]$

asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 63 views

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CAT 2021 Set-1 | Quantitative Aptitude | Question: 8
$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if $ – 2 < x < 3 \; \text{or} \; x > 9 $ $ x < – 5 \; \text{or} \; 3 < x < 9 $ $ – 5 < x < – 2 \; \text{or} \; 3 < x < 9 $ $ x < – 5 \; \text{or} \; – 2 < x < 3 $

$f(x) = \dfrac{x^{2} + 2x – 15}{x^{2} – 7x – 18}$ is negative if and only if $ – 2 < x < 3 \; \text{or} \; x > 9 $ $ x < – 5 \; \text{or} \; 3 < x < 9 $ $ – 5 < x < – 2 \; \text{or} \; 3 < x < 9 $ $ x < – 5 \; \text{or} \; – 2 < x < 3 $

asked Jan 19 in Quantitative Aptitude soujanyareddy13 2.7k points 54 views

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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 $0$ $15.9375$ $3$ $14.0625$

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

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 128 views

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CAT 2020 Set-2 | Question: 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 $1$ $16$ $0$ $4$

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 $1$ $16$ $0$ $4$

asked Sep 17, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 89 views

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CAT 2020 Set-1 | Question: 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 $0$ $40$ $10$ $20$

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 $0$ $40$ $10$ $20$

asked Sep 16, 2021 in Quantitative Aptitude soujanyareddy13 2.7k points 110 views

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CAT 2019 Set-2 | Question: 95
Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$ and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $f (24) = 54$, then $f (18)$ equals _______

Let $f$ be a function such that $f (mn) = f (m) f (n)$ for every positive integers $m$ and $n$. If $f (1), f (2)$ and $f (3)$ are positive integers, $f (1) < f (2),$ and $f (24) = 54$, then $f (18)$ equals _______

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 181 views

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CAT 2018 Set-1 | Question: 93
If $f(x+2)=f(x)+f(x+1)$ for all positive integers $x$, and $f(11)=91,f(15)=617$, then $f(10)$ equals ________

If $f(x+2)=f(x)+f(x+1)$ for all positive integers $x$, and $f(11)=91,f(15)=617$, then $f(10)$ equals ________

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 193 views

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CAT 2017 Set-2 | Question: 89
Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$ at $x=1$ is $16$ $18$ $36$ $40$

Let $f\left ( x \right )=x^{2}$ and $g\left ( x \right )=2^{x}$, for all real $x$. Then the value of $ f \left ( f\left ( g\left ( x \right ) \right )+g\left( f\left ( x \right ) \right ) \right)$ at $x=1$ is $16$ $18$ $36$ $40$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 152 views

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CAT 2017 Set-2 | Question: 98
Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ if and only if $5/2<x<7/2$ $x\leq 5/2$ or $x\geq 7/2$ $x< 5/2$ or $x\geq 7/2$ $5/2\leq x\leq 7/2$

Let $f\left ( x \right )=2x-5$ and $g\left ( x \right )=7-2x.$ Then $ \mid f\left ( x \right ) + g\left ( x \right ) \mid=\mid f(x) \mid + \mid g\left ( x \right ) \mid$ if and only if $5/2<x<7/2$ $x\leq 5/2$ or $x\geq 7/2$ $x< 5/2$ or $x\geq 7/2$ $5/2\leq x\leq 7/2$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 191 views

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CAT 2017 Set-2 | Question: 97
If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$

If $f\left ( ab \right )=f\left ( a \right )f\left ( b \right )$ for all positive integers $a$ and $b$, then the largest possible value of $f\left (1\right )$ is $1$ $2$ $0$ $3$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 125 views

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CAT 2017 Set-1 | Question: 99
If $f( x)=\dfrac{5x+2}{ 3x-5}$ and $g( x )=x^{2}-2x-1,$ then the value of $g( f( f( 3 ) ) )$ is $2$ $1/3$ $6$ $2/3$

If $f( x)=\dfrac{5x+2}{ 3x-5}$ and $g( x )=x^{2}-2x-1,$ then the value of $g( f( f( 3 ) ) )$ is $2$ $1/3$ $6$ $2/3$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 139 views

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CAT 2016 | Question: 73
$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows. $A(x, y) = x + y$ $M(x, y) = xy$ $S(x,y)= x-y$ $D(x,y)= x/y, y\neq 0$ What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$? $60$ $140$ $25$ $70$

$A, S, M$ and $D$ are functions of $x$ and $y$, and they are defined as follows. $A(x, y) = x + y$ $M(x, y) = xy$ $S(x,y)= x-y$ $D(x,y)= x/y, y\neq 0$ What is the value of $M(M(A(M(x, y), S(y, x)), x), A(y, x))$ for $x = 2, y = 3$? $60$ $140$ $25$ $70$

asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 260 views

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CAT 2015 | Question: 81
The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ ... $n \geq 1$. What is the value of $g\left ( 1 \right )?$ $0$ $2$ $1$ Cannot be determined

The set of all positive integers is the union of two disjoint subsets$:\left \{ f\left ( 1 \right ),f\left ( 2 \right ), \dots, f\left ( n \right ), \dots \right \}$ and $\left \{ g\left ( 1 \right ),g\left ( 2 \right ), \dots, g\left ( n \right ), \dots \right \}$, ... $n \geq 1$. What is the value of $g\left ( 1 \right )?$ $0$ $2$ $1$ Cannot be determined

asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 189 views

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CAT 2015 | Question: 82
For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________

For all non-negative integers $x$ and $y$, $f(x,y)$ is defined as below. $f( 0,y) = y+1$ $f(x+1,0) = f( x, 1)$ $f( x+1, y+1) = f\left( x,f( x+1,y) \right)$ Then what is the value of $f(1,2)$ ________

asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 1.9k views

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CAT 2011 | Question: 4
$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if $n$ is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$ If $f_1(1)=0$, then what is $f_{50}(1)$? $-18$ $-16$ $-17$ Cannot be determined

$\begin{array}{}Let\;f_{n+1}(x)&=f_n(x)+1\;\text{if $n$ is a multiple of 3}\\ &=f_n(x)-1\;\text{otherwise.}\end{array}$ If $f_1(1)=0$, then what is $f_{50}(1)$? $-18$ $-16$ $-17$ Cannot be determined

asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 262 points 258 views

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CAT 2011 | Question: 20
Consider the function given by $f(x) =\mid x-1\mid-x$ What is the area of the triangle bounded by the graph of the given function with the coordinate axis given by $x=0\:\text{and}\:y=0$? $2$ $\large\frac{1}{4}$ $\large\frac{1}{2}$ $1$

Consider the function given by $f(x) =\mid x-1\mid-x$ What is the area of the triangle bounded by the graph of the given function with the coordinate axis given by $x=0\:\text{and}\:y=0$? $2$ $\large\frac{1}{4}$ $\large\frac{1}{2}$ $1$

asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 262 points 171 views

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CAT 2011 | Question: 17
The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true? $g(x)=[f(x)]$ $g(x)=f(-x)$ $g(x)=-f(x)$ None of these

The graphs given alongside represent two functions $f(x)\:\text{and}\:g(x)$ respectively. Which of the following is true? $g(x)=[f(x)]$ $g(x)=f(-x)$ $g(x)=-f(x)$ None of these

asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 262 points 166 views

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CAT 2011 | Question: 21
Consider the function given by $f(x) =\mid x-1\mid-x$ Which of the following is not true about the graph of $f(x)$? A portion of the graph is parallel to the line $y = 25$. A portion of graph is in 2nd quadrant. Some portion of graph lies in 1st quadrant. Some portion of graph lies in 3rd quadrant.

Consider the function given by $f(x) =\mid x-1\mid-x$ Which of the following is not true about the graph of $f(x)$? A portion of the graph is parallel to the line $y = 25$. A portion of graph is in 2nd quadrant. Some portion of graph lies in 1st quadrant. Some portion of graph lies in 3rd quadrant.

asked Mar 9, 2020 in Quantitative Aptitude Krithiga2101 262 points 169 views

1 vote

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CAT 2019 Set-1 | Question: 87
For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals _______

For any positive integer $n$, let $f(n)=n(n+1)$ if n is even, and $f(n)=n+3$ if n is odd. if $m$ is a positive integer such that $8f(m+1)-f(m)=2$, then $m$ equals _______

asked Mar 8, 2020 in Quantitative Aptitude go_editor 13.3k points 244 views

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CAT 2019 Set-1 | Question: 90
Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______

Consider a function $f$ satisfying $f(x+y)=f(x)f(y)$ where $x,y$ are positive integers, and $f(1)=2$. If $f(a+1)+f(a+2)+\ldots +f(a+n)=16(2^{n}-1)$ then $a$ is equal to ______

asked Mar 8, 2020 in Quantitative Aptitude go_editor 13.3k points 157 views

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CAT 2013 | Question: 23
If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will be maximum when $p>0,q>0$ minimum when $p<0,q<0$ minimum when $p>0,q<0$ maximum when $p>0,q<0$

If $g(x)=p\mid x \mid-qx^2$, where $p$ and $q$ are constants, then at $x=0, g(x)$ will be maximum when $p>0,q>0$ minimum when $p<0,q<0$ minimum when $p>0,q<0$ maximum when $p>0,q<0$

asked Mar 6, 2020 in Quantitative Aptitude admin 2.4k points 206 views

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CAT 2013 | Question: 29
Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true? domain of $(f+g)=R-(-2,-1]$ domain of $(f+g)=R-[-1,0)$ ... Both II and IV Both I and III Both I and IV Both II and III

Let $f(x)= \dfrac{1}{1+x^2}$ and $g(x)=\dfrac{e^{−x}}{1+[x]}$, where $[x]$ is the greatest integer less than or equal to $x$. Then which of the following domain is true? domain of $(f+g)=R-(-2,-1]$ domain of $(f+g)=R-[-1,0)$ ... Both II and IV Both I and III Both I and IV Both II and III

asked Mar 6, 2020 in Quantitative Aptitude admin 2.4k points 157 views

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CAT 2010 | Question: 16
Let $f$ be an injective map with domain $\left \{ x, y, z \right \}$ and the range $\left \{ 1, 2, 3 \right \}$ such that exactly one of the following statements is correct and the remaining are false. $f\left \{x \right \}=1,f\left ( y \right )\neq 1,f\left ( z \right )\neq 2.$ The value of $f^{-1}\left ( 1 \right )$ is $x$ $y$ $z$ None of the above

Let $f$ be an injective map with domain $\left \{ x, y, z \right \}$ and the range $\left \{ 1, 2, 3 \right \}$ such that exactly one of the following statements is correct and the remaining are false. $f\left \{x \right \}=1,f\left ( y \right )\neq 1,f\left ( z \right )\neq 2.$ The value of $f^{-1}\left ( 1 \right )$ is $x$ $y$ $z$ None of the above

asked Mar 1, 2020 in Quantitative Aptitude Arjun 8.3k points 121 views

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CAT 1999 | Question: 100
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following expressions yields $x^2$ as a result? $F(f(x, -x)).G(f(x, -x))$ $F(f(x, x)).G(f(x, x)).4$ $-F(f(x, x)).G(f(x, -x)) \: \log_2 16$ $f(x,x).f(x,x)$

Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following expressions yields $x^2$ as a result? $F(f(x, -x)).G(f(x, -x))$ $F(f(x, x)).G(f(x, x)).4$ $-F(f(x, x)).G(f(x, -x)) \: \log_2 16$ $f(x,x).f(x,x)$

asked May 14, 2016 in Logical Reasoning go_editor 13.3k points 244 views

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CAT 1999 | Question: 98
Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following statements is true? $F(f(x,y)) .G(f(x,y)) = -F(f(x,y)).G(f(x,y))$ ... $F(f(x,y)) .G(f(x,y)) \neq G(f(x,y)).F(f(x,y))$ $F(f(x,y)) +G(f(x,y)) + f(x,y)= f(-x,-y)$

Answer the question based on the information given below: Let x and y be real numbers and let $f(x, y) = |x+y|, F(f(x, y)) = -f(x,y) \text{ and } G(f(x, y)) = -F(f(x, y))$ Which of the following statements is true? $F(f(x,y)) .G(f(x,y)) = -F(f(x,y)).G(f(x,y))$ $F(f(x,y)) .G(f(x,y)) > -F(f(x,y)).G(f(x,y))$ $F(f(x,y)) .G(f(x,y)) \neq G(f(x,y)).F(f(x,y))$ $F(f(x,y)) +G(f(x,y)) + f(x,y)= f(-x,-y)$

asked May 14, 2016 in Logical Reasoning go_editor 13.3k points 273 views

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CAT 2000 | Question: 76
Answer the following question based on the information given below. For real numbers $x, y,$ ... $x$ and $y$ are less than $-1$ Both $x$ and $y$ are positive Both $x$ and $y$ are negative $y > x$

Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... than $g(x, y)?$ Both $x$ and $y$ are less than $-1$ Both $x$ and $y$ are positive Both $x$ and $y$ are negative $y > x$

asked May 1, 2016 in Quantitative Aptitude go_editor 13.3k points 390 views

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29

CAT 2000 | Question: 79
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $(h(x, y, z) - f(x, y, z))/(n(x, y, z) - g(x, y, z))$

Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$ ... $(h(x, y, z) - f(x, y, z))/(n(x, y, z) - g(x, y, z))$

asked May 1, 2016 in Quantitative Aptitude go_editor 13.3k points 230 views

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30

CAT 2000 | Question: 78
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $(j(x, y, z) - g(x, y, z))/h(x, y, z)$ $(f(x, y, z) - h(x, y, z))/f(x, y, z)$

Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$ ... $(j(x, y, z) - g(x, y, z))/h(x, y, z)$ $(f(x, y, z) - h(x, y, z))/f(x, y, z)$

asked May 1, 2016 in Quantitative Aptitude go_editor 13.3k points 671 views

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31

CAT 2014 | Question: 33
Use the following information for next two questions: A function $f(x)$ is said to be even if $f(-x) = f(x)$, and odd if $f(-x) = -f(x)$. Thus, for example, the function given by $f(x)=x^{2}$ is even, while the ... questions. The sum of two odd functions is always an even function is always an odd function is sometimes odd and sometimes even may be neither odd nor even

Use the following information for next two questions: A function $f(x)$ is said to be even if $f(-x) = f(x)$, and odd if $f(-x) = -f(x)$. Thus, for example, the function given by $f(x)=x^{2}$ is even, while the function given by ... following questions. The sum of two odd functions is always an even function is always an odd function is sometimes odd and sometimes even may be neither odd nor even

asked Apr 27, 2016 in Quantitative Aptitude go_editor 13.3k points 355 views

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32

CAT 2000 | Question: 88
Answer the following question based on the information given below. For a real number $x,$ let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... $r$ is an integer $\geq 2.$ Then what is the value of $f^{r-1}(-r) + f^r(-r)+f^{r+1}(-r)$? $-1$ $0$ $1$ None of these

Answer the following question based on the information given below. For a real number $x,$ let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... $r$ is an integer $\geq 2.$ Then what is the value of $f^{r-1}(-r) + f^r(-r)+f^{r+1}(-r)$? $-1$ $0$ $1$ None of these

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 169 views

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33

CAT 2000 | Question: 84
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 217 views

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34

CAT 2000 | Question: 83
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

asked Apr 25, 2016 in Quantitative Aptitude go_editor 13.3k points 162 views

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35

CAT 2000 | Question: 107
For all non-negative integers $x$ and $y, f(x, y)$ is defined as below $f(0, y) = y + 1$ $f(x + 1, 0) = f(x, 1)$ $f(x + 1,y + 1) = f(x, f(x + 1, y))$ Then, what is the value of $f(1, 2)?$ Two Four Three Cannot be determined

For all non-negative integers $x$ and $y, f(x, y)$ is defined as below $f(0, y) = y + 1$ $f(x + 1, 0) = f(x, 1)$ $f(x + 1,y + 1) = f(x, f(x + 1, y))$ Then, what is the value of $f(1, 2)?$ Two Four Three Cannot be determined

asked Mar 30, 2016 in Quantitative Aptitude go_editor 13.3k points 287 views

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36

CAT 2000 | Question: 105
The set of all positive integers is the union of two disjoint subsets $\{f(1), f(2),\dots ,f(n),\dots\}$ and $\{g(1), g(2),\dots,g(n),\dots\},$ where $f(1) < f(2) <\dots < f(n) < \dots,$ and $g(1) < g(2) <\dots< g(n) < \dots,$ and $g(n) = f(f(n)) + 1$ for all $n \geq 1.$ What is the value of $g(1)?$ Zero Two One Cannot be determined

The set of all positive integers is the union of two disjoint subsets $\{f(1), f(2),\dots ,f(n),\dots\}$ and $\{g(1), g(2),\dots,g(n),\dots\},$ where $f(1) < f(2) <\dots < f(n) < \dots,$ and $g(1) < g(2) <\dots< g(n) < \dots,$ and $g(n) = f(f(n)) + 1$ for all $n \geq 1.$ What is the value of $g(1)?$ Zero Two One Cannot be determined

asked Mar 30, 2016 in Quantitative Aptitude go_editor 13.3k points 660 views

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37

CAT 2000 | Question: 87
Answer the following question based on the information given below. For a real number $x$, let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$? $\frac{1}{3}$ $3$ $\frac{1}{18}$ None of these

Answer the following question based on the information given below. For a real number $x$, let f(x) = 1/(1 + x), if x is non-negative = 1+ x, if x is negative f$^n$(x) = f(f$^{n – 1}$(x)), n = 2, 3, .... What is the value of the product, $f(2)f^2(2)f^3(2)f^4(2)f^5(2)$? $\frac{1}{3}$ $3$ $\frac{1}{18}$ None of these

asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 140 views

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38

CAT 2000 | Question: 82
Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

Answer the following question based on the information given below. Given below is a graph made up of straight-line segments shown as thick lines. Choose the answer as if $f(x) = 3 f(–x);$ if $f(x) = –f(–x);$ if $f(x) = f(–x);$ and if $3 f(x) = 6 f(–x),$ for $x\geq 0.$ $1$ $2$ $3$ $4$

asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 127 views

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39

CAT 2000 | Question: 77
Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ ... $f(x, y, z)/g(x, y, z)$ $(f(x, y, z) + h(x, y, z) - g(x, y, z))/j(x, y, z)$

Answer the following question based on the information given below. For three distinct real numbers $x, y$ and $z,$ let $f(x, y, z) = \min(\max(x, y), \max(y, z), \max(z, x))$ $g(x, y, z) = \max(\min(x, y), \min(y, z), \min(z, x))$ $h(x, y, z) = \max(\max(x, y), \max(y, z), \max(z, x))$ ... $j(x, y, z)/h(x, y, z)$ $f(x, y, z)/g(x, y, z)$ $(f(x, y, z) + h(x, y, z) - g(x, y, z))/j(x, y, z)$

asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 168 views

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40

CAT 2000 | Question: 75
Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... $f(x, y) - (g(x, y))^2$ $g(x, y) - (f(x, y))^2$ $f(x, y) + g(x, y)$

Answer the following question based on the information given below. For real numbers $x, y,$ let $f(x, y) = \left\{\begin{matrix} \text{Positive square-root of}\; (x + y),\;\text{if}\; (x + y)^{0.5}\;\text{is real} \\ (x + y)^2,\;\text{otherwise} \end{matrix}\right.$ ... $f(x, y) - (g(x, y))^2$ $g(x, y) - (f(x, y))^2$ $f(x, y) + g(x, y)$

asked Mar 29, 2016 in Quantitative Aptitude go_editor 13.3k points 215 views

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