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Recent questions tagged algebra
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41
CAT 2012 | Question: 13
If $a= \dfrac{x}{y+z},b= \dfrac{y}{z+y},c= \dfrac{z}{x+y}$, then which of the following statements is/are true? $\dfrac{b+c-1}{yz}+\dfrac{a+c-1}{xz}+\dfrac{a+b-1}{yx}=1 \\$ $\dfrac{x^{2}}{a(1-bc)}= \dfrac{y^{2}}{b(1-ca)}= \dfrac{z^{2}}{c(1-ab)} \\$ $(a+b)c+(b+c)a+(a+c)b= \dfrac{2(x+y+z)(xy+xz+yz)-6xyz}{(x+y)(y+z)(z+x)}$ I and II I and III II and III None of these
Chandanachandu
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in
Quantitative Aptitude
Mar 5, 2020
by
Chandanachandu
308
points
213
views
cat2012
quantitative-aptitude
algebra
1
vote
1
answer
42
CAT 2010 | Question: 1
If $r, s$ and $t$ are consecutive odd integers with $r < s < t$, which of the following must be true? $rs = t$ $r + t = 2t – s$ $r + s = t – 2$ $r + t = 2s$
Arjun
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in
Quantitative Aptitude
Mar 1, 2020
by
Arjun
8.3k
points
488
views
cat2010
quantitative-aptitude
algebra
1
vote
0
answers
43
CAT 2010 | Question: 8
Consider the following statements: If $a^{x}=b,b^{y}=c,c^{z}=a,$ then $xyz=1$ If $p=a^{x},q=a^{y},\left ( p^{y}q^{y} \right )^{z}=a^{2},$ then $xyz=1$ If $x^{a}=y^{b}=z^{c}$ and $ab+bc+ca=0$ then $xyz=1$ Of these statements: I and II are correct II and III are correct Only I is correct All I, II and III are correct
Arjun
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in
Quantitative Aptitude
Mar 1, 2020
by
Arjun
8.3k
points
205
views
cat2010
quantitative-aptitude
algebra
0
votes
1
answer
44
CAT 2003 | Question: 2-89
If three positive real numbers $x, y, z$ satisfy $y – x = z – y$ and $x y z = 4,$ then what is the minimum possible value of $y?$ $2^{\frac{1}{3}}$ $2^{\frac{2}{3}}$ $2^{\frac{1}{4}}$ $2^{\frac{3}{4}}$
go_editor
asked
in
Quantitative Aptitude
May 5, 2016
by
go_editor
13.4k
points
204
views
cat2003-2
quantitative-aptitude
algebra
0
votes
1
answer
45
CAT 2003 | Question: 2-81
Two binary operations $\oplus$ and $*$ are defined over the set $\{a, e, f, g, h\}$ as per the following tables $\oplus$ a e f g h a a e f g h e e f g h a f f g h a e g g h a e f h h a e f g $\ast$ a e f g h a a a a a a e a e f g h f a ... $\{ a10 \ast (f10 \oplus g9)\} \oplus e^8$ equals $e$ $f$ $g$ $h$
go_editor
asked
in
Quantitative Aptitude
May 5, 2016
by
go_editor
13.4k
points
361
views
cat2003-2
quantitative-aptitude
algebra
0
votes
1
answer
46
CAT 2003 | Question: 2-80
Two binary operations $\oplus$ and $^ \ast $ are defined over the set $\{a, e, f, g, h\}$ as per the following tables $\oplus$ a e f g h a a e f g h e e f g h a f f g h a e g g h a e f h h a e f g $\ast$ a e f g h a a a a a a e a e f g ... $ f \oplus \left[f \ast \{ f \oplus (f \ast f )\} \right]$ equal $e$ $f$ $g$ $h$
go_editor
asked
in
Quantitative Aptitude
May 5, 2016
by
go_editor
13.4k
points
377
views
cat2003-2
quantitative-aptitude
algebra
0
votes
1
answer
47
CAT 2003 | Question: 2-79
Two binary operations $\oplus$ and $^\ast$ are defined over the set $\{a, e, f, g, h\}$ as per the following tables $\oplus$ a e f g h a a e f g h e e f g h a f f g h a e g g h a e f h h a e f g $^\ast$ a e f g h a a a a a a e a e f g h f a ... $f^2 = f\ast f, \: g^3 = g \ast g \ast g$, and so on. What is the smallest positive integer n such that $g^n = e?$ $4$ $5$ $2$ $3$
go_editor
asked
in
Quantitative Aptitude
May 5, 2016
by
go_editor
13.4k
points
450
views
cat2003-2
quantitative-aptitude
algebra
0
votes
1
answer
48
CAT 2003 | Question: 2-57
Let $x$ and $y$ be positive integers such that $x$ is prime and $y$ is composite. Then, $y – x$ cannot be an even integer $xy$ cannot be an even integer. $\frac{x+y}{x}$ cannot be an even integer None of these.
go_editor
asked
in
Quantitative Aptitude
May 4, 2016
by
go_editor
13.4k
points
594
views
cat2003-2
quantitative-aptitude
algebra
0
votes
1
answer
49
CAT 2003 | Question: 2-54
If $a, a + 2$ and $a + 4$ are prime numbers, then the number of possible solutions for $a$ is: one two three more than three
go_editor
asked
in
Quantitative Aptitude
May 4, 2016
by
go_editor
13.4k
points
237
views
cat2003-2
quantitative-aptitude
algebra
0
votes
1
answer
50
CAT 2003 | Question: 2-53
Let $a, b, c, d$ and $e$ be integers such that $a = 6b = 12c,$ and $2b = 9d = 12e.$ Then which of the following pairs contains a number that is not an integer? $\left[ \frac{a}{27}, \frac{b}{e} \right] $ $\left[ \frac{a}{36}, \frac{c}{e} \right] $ $\left[ \frac{a}{12}, \frac{bd}{18} \right] $ $\left[ \frac{a}{6}, \frac{c}{d} \right] $
go_editor
asked
in
Quantitative Aptitude
May 4, 2016
by
go_editor
13.4k
points
3.7k
views
cat2003-2
quantitative-aptitude
algebra
0
votes
0
answers
51
CAT 2000 | Question: 74
$\text{A, B, C}$ are three numbers. Let
[email protected]
\text{(A, B)} =$ average of $\text{A}$ and $\text{B}$, $/ \text{(A, B)} = $ product of $\text{A}$ and $\text{B}$, and $\text{X(A, B)} = $ the result of dividing $\text{A}$ by $\text{B}$ Average of $\text{A, B}$ and $\text{C}$ ... $/(@(\text{X(}@\text{(B, A)}, 2), \text{C)}, 3)$ $/(\text{X(}@(/(@\text{(B, A)}, 2), \text{C)}, 3), 2)$
go_editor
asked
in
Quantitative Aptitude
May 1, 2016
by
go_editor
13.4k
points
689
views
cat2000
quantitative-aptitude
algebra
0
votes
0
answers
52
CAT 2001 | Question: 42
Let $b$ be a positive integer and $a = b^2 – b$. If b $\geq$ 4, then $a^2 – 2a$ is divisible by $15$ $20$ $24$ None of these
go_editor
asked
in
Quantitative Aptitude
Apr 1, 2016
by
go_editor
13.4k
points
195
views
cat2001
quantitative-aptitude
algebra
0
votes
1
answer
53
CAT 2001 | Question: 37
Let $x, y$ be two positive numbers such that $x + y =1.$ Then, the minimum value of $\left(x+ \frac{1}{x} \right)^2 + \left(y + \frac{1}{y}\right)^2$ is $12$ $20$ $12.5$ $13.3$
go_editor
asked
in
Quantitative Aptitude
Mar 31, 2016
by
go_editor
13.4k
points
1.2k
views
cat2001
quantitative-aptitude
algebra
0
votes
0
answers
54
CAT 2001 | Question: 27
If $a, b, c$ and $d$ are four positive real numbers such that $abcd = 1,$ what is the minimum value of $(1 + a)(1 + b)(1 + c)(1 + d)?$ $4$ $1$ $16$ $18$
go_editor
asked
in
Quantitative Aptitude
Mar 31, 2016
by
go_editor
13.4k
points
130
views
cat2001
quantitative-aptitude
algebra
0
votes
0
answers
55
CAT 2001 | Question: 15
$m$ is the smallest positive integer such that for any integer $n > m,$ the quantity $n^3 – 7n^2 + 11n – 5$ is positive. What is the value of $m?$ $4$ $5$ $8$ None of these
go_editor
asked
in
Quantitative Aptitude
Mar 31, 2016
by
go_editor
13.4k
points
150
views
cat2001
quantitative-aptitude
algebra
0
votes
1
answer
56
CAT 2001 | Question: 3
Let $x, y$ and $z$ be distinct integers, $x$ and $y$ are odd and positive, and $z$ is even and positive. Which one of the following statements cannot be true? $(x − z)^2y$ is even $(x − z)^2y$ is odd $(x − y)y$ is odd $(x − y)^2z$ is even
go_editor
asked
in
Quantitative Aptitude
Mar 31, 2016
by
go_editor
13.4k
points
729
views
cat2001
quantitative-aptitude
algebra
1
vote
0
answers
57
CAT 2000 | Question: 73
$\text{A, B, C}$ are three numbers. Let
[email protected]
\text{(A, B)} =$ average of $\text{A}$ and $\text{B}$, $/ \text{(A, B)} = $ product of $\text{A}$ and $\text{B}$, and $\text{X(A, B)} = $ the result of dividing $\text{A}$ by $\text{B}$ The sum of $\text{A}$ and $\text{B}$ is given by $/(@\text{(A, B)}, 2)$ $X(@\text{(A, B)}, 2)$
[email protected]
(/\text{(A, B)}, 2)$
[email protected]
(X\text{(A, B)}, 2)$
go_editor
asked
in
Quantitative Aptitude
Mar 28, 2016
by
go_editor
13.4k
points
980
views
cat2000
quantitative-aptitude
algebra
0
votes
0
answers
58
CAT 2000 | Question: 70
Each of the numbers $x_1, x_2,\dots, x_n, n > 4,$ is equal to $1$ or $–1.$ Suppose, $x_1x_2x_3x_4 + x_2x_3x_4x_5 + x_3x_4x_5x_6 + \dots + x_{n–3}x_{n–2}x_{n–1}x_n + x_{n–2}x_{n–1}x_nx_1+ x_{n–1}x_nx_1x_2 + x_nx_1x_2x_3= 0$, then, $n$ is even. $n$ is odd. $n$ is an odd multiple of $3.$ $n$ is prime
go_editor
asked
in
Quantitative Aptitude
Mar 28, 2016
by
go_editor
13.4k
points
196
views
cat2000
quantitative-aptitude
algebra
0
votes
1
answer
59
CAT 2000 | Question: 65
Let $x, y$ and $z$ be distinct integers, that are odd and positive. Which one of the following statements cannot be true? $xyz^2$ is odd. $(x − y)^2 z$ is even. $(x + y − z)^2 (x + y)$ is even. $(x − y) (y + z) (x + y − z)$ is odd
go_editor
asked
in
Quantitative Aptitude
Mar 28, 2016
by
go_editor
13.4k
points
441
views
cat2000
quantitative-aptitude
algebra
0
votes
0
answers
60
CAT 2000 | Question: 57
$\begin{array}{|c|c|c|c|c|c|c|c|} \hline x & 1 & 2 & 3 & 4 & 5 & 6 \\\hline y & 4 & 8 & 14 & 22 & 32 & 44 \\\hline \end{array}$ In the above table, for suitably chosen constants $a, b$ and $c,$ which one of ... best describes the relation between $y$ and $x?$ $y = a + bx$ $y = a + bx + cx^2$ $y = e^{a + bx}$ None of the above
go_editor
asked
in
Quantitative Aptitude
Mar 26, 2016
by
go_editor
13.4k
points
271
views
cat2000
quantitative-aptitude
algebra
0
votes
0
answers
61
CAT 2002 | Question: 96
If $pqr=1$ then $\frac{1}{1+p+r^{-1}} + \frac{1}{1+q+r^{-1}} + \frac{1}{1+r+p^{-1}} $ is equivalent to $p+q+r$ $\frac{1}{p+q+r}$ $1$ $p^{-1}+q^{-1}+r^{-1}$
go_editor
asked
in
Quantitative Aptitude
Mar 2, 2016
by
go_editor
13.4k
points
237
views
cat2002
quantitative-aptitude
algebra
0
votes
0
answers
62
CAT 2002 | Question: 57
If $x^2 + 5y^2 + z^2 = 2y(2x+z)$, then which of the following statements are necessarily true? $x=2y$ $x=2z$ $2x=z$ Only I Only II Only III Only I and II
go_editor
asked
in
Quantitative Aptitude
Mar 1, 2016
by
go_editor
13.4k
points
150
views
cat2002
quantitative-aptitude
algebra
0
votes
0
answers
63
CAT 2002 | Question: 53
For three integers $x, y$ and $z, x+y+z=15,$ and $xy+yz+xz=3.$ What is the largest value which $x$ can take? $3 \sqrt{13}$ $\sqrt{19}$ $13 /3$ $\sqrt{15}$
go_editor
asked
in
Quantitative Aptitude
Mar 1, 2016
by
go_editor
13.4k
points
224
views
cat2002
quantitative-aptitude
algebra
0
votes
0
answers
64
CAT 2003 | Question: 1-147
if $x,y,z$ are distinct positive real numbers then $\frac{x^2(y+z) + y^2(x+z) + z^2(x+y)}{xyz}$ would be greater than $4$ greater than $5$ greater than $6$ None of these
go_editor
asked
in
Quantitative Aptitude
Feb 10, 2016
by
go_editor
13.4k
points
239
views
cat2003-1
quantitative-aptitude
algebra
0
votes
0
answers
65
CAT 2003 | Question: 1-131
Let $a, b, c, d$ be the four integers such that $a +b+c+d =4m+1$ where m is a positive integer. Given $m,$ which one of the following is necessarily true? The minimum possible value of $a^2 + b^2 + c^2 + d^2$ is $4m^2 - 2m + 1$ ... $4m^2 - 2m + 1$ The maximum possible value of $a^2 + b^2 + c^2 + d^2$ is $4m^2 + 2m + 1$
go_editor
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in
Quantitative Aptitude
Feb 8, 2016
by
go_editor
13.4k
points
227
views
cat2003-1
quantitative-aptitude
algebra
0
votes
0
answers
66
CAT 2003 | Question: 1-121
Choose $1$ if the question can be answered by one of the statements alone but not by the other. Choose $2$ if the question can be answered by using either statement alone. Choose $3$ if the question can be answered by using both the statements together, but cannot be answered by ... $a=2$ and $b$ is an integer? $b$ is even $b$ is greater than $16$
go_editor
asked
in
Quantitative Aptitude
Feb 7, 2016
by
go_editor
13.4k
points
200
views
cat2003-1
quantitative-aptitude
algebra
0
votes
2
answers
67
CAT 2003 | Question: 1-105
The number of non-negative real roots of $2^x - x - 1 =0$ equals _______ $0$ $1$ $2$ $3$
go_editor
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in
Quantitative Aptitude
Feb 5, 2016
by
go_editor
13.4k
points
647
views
cat2003-1
quantitative-aptitude
algebra
0
votes
1
answer
68
CAT 2004 | Question: 50
Let $y=\frac{1}{2+ \frac{1}{3+ \frac{1}{2+ \frac{1}{3+ \dots } } } }$ what is the value of $y?$ $\frac{\sqrt{13} +3} {2}$ $\frac{\sqrt{13} -3} {2}$ $\frac{\sqrt{15} +3} {2}$ $\frac{\sqrt{15} -3} {2}$
go_editor
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in
Quantitative Aptitude
Jan 12, 2016
by
go_editor
13.4k
points
303
views
cat2004
quantitative-aptitude
algebra
0
votes
1
answer
69
CAT 2004 | Question: 49
If $\frac{a}{a+b} = \frac{b}{c+a} = \frac{c}{a+b} = r$, then $r$ cannot take any value except $1/2$ $-1$ $1/2$ or $-1$ -$1/2$ or $-1$
go_editor
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in
Quantitative Aptitude
Jan 12, 2016
by
go_editor
13.4k
points
270
views
cat2004
quantitative-aptitude
algebra
0
votes
1
answer
70
CAT 2004 | Question: 46
The total number of integer pairs $(x,y)$ satisfying the equation $x+y=xy$ is $0$ $1$ $2$ None of these
go_editor
asked
in
Quantitative Aptitude
Jan 12, 2016
by
go_editor
13.4k
points
283
views
cat2004
quantitative-aptitude
algebra
0
votes
0
answers
71
CAT 2009 | Question: 16
If $x=1+2a+3a^{2}+4a^{2}+\dots(-1 < a < 1)$ and $y=1+3b+6b^{2}+10b^{3}+\dots(-1 < b < 1),$ then find $1+ab+(ab)^{2}+(ab)^{3}+\dots$ in terms of $x$ and $y$. $\frac{x^{1/2} y^{1/3}}{x^{1/2}+y^{1/3}-1}$ $\frac{xy}{x+y-1}$ $\frac{x^{1/3}y^{2/3}}{x^{1/3}+y^{1/2}-1}$ None of these.
makhdoom ghaya
asked
in
Quantitative Aptitude
Dec 31, 2015
by
makhdoom ghaya
7.9k
points
224
views
cat2009
quantitative-aptitude
algebra
0
votes
0
answers
72
CAT 2005 | Question: 26
Let $x=\sqrt{4+\sqrt{4-\sqrt{4+\sqrt{4-}}}} \dots$ to infinity. Then $x$ equals $3$ $\frac{\sqrt{13} -1}{2}$ $\frac{\sqrt{13} +1}{2}$ $\sqrt{13}$
go_editor
asked
in
Quantitative Aptitude
Dec 29, 2015
by
go_editor
13.4k
points
304
views
cat2005
quantitative-aptitude
algebra
0
votes
1
answer
73
CAT 2005 | Question: 08
If $\text{R} = \dfrac{30^{65} – 29^{65}}{30^{64} + 29^{64}}$ then $0 < \text{R} \leq 0.1$ $0.1 < \text{R} \leq 0.5$ $0.5 < \text{R} \leq 1.0$ $\text{R} > 1.0$
go_editor
asked
in
Quantitative Aptitude
Dec 29, 2015
by
go_editor
13.4k
points
1.1k
views
cat2005
quantitative-aptitude
algebra
0
votes
1
answer
74
CAT 2006 | Question: 58
The number of solutions of the equation $2x+y=40$ where both $x$ and $y$ are positive integers and $x \leq y$ is: $7$ $13$ $14$ $18$ $20$
go_editor
asked
in
Quantitative Aptitude
Dec 28, 2015
by
go_editor
13.4k
points
308
views
cat2006
quantitative-aptitude
algebra
0
votes
0
answers
75
CAT 2006 | Question: 57
What are the values of $x$ and $y$ that satisfy both the equations? $2^{0.7x} \cdot 3^{-1.25y} = 8\sqrt{6} / 27$ $4^{0.3x} \cdot 9^{0.2y} = 8.(81)^{\frac{1}{5}}$ $x=2, y=5$ $x=2.5, y=6$ $x=3, y=5$ $x=3, y=4$ $x=5, y=2$
go_editor
asked
in
Quantitative Aptitude
Dec 28, 2015
by
go_editor
13.4k
points
282
views
cat2006
quantitative-aptitude
algebra
0
votes
1
answer
76
CAT 2006 | Question: 53
If $a/b=1/3, b/c=2, c/d=1/2, d/e=3$ and $e/f=1/4$ then what is the value of $abc/def?$ $3/8$ $27/8$ $3/4$ $27/4$ $1/4$
go_editor
asked
in
Quantitative Aptitude
Dec 28, 2015
by
go_editor
13.4k
points
196
views
cat2006
quantitative-aptitude
algebra
2
votes
2
answers
77
CAT 2007 | Question: 21
How many pairs of positive integers, $m, n$ satisfy $1/m +4/n=1/12$ where $n$ is an odd integer less than $60?$ $6$ $4$ $7$ $5$ $3$
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in
Quantitative Aptitude
Dec 7, 2015
by
go_editor
13.4k
points
371
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cat2007
quantitative-aptitude
algebra
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