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Recent questions tagged algebra

1 vote
1 answer
1
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 5 88 353 102 views
1 vote
1 answer
2
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 5 88 353 155 views
0 votes
0 answers
3
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 5 88 353 33 views
2 votes
1 answer
4
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 5 88 353 133 views
2 votes
1 answer
5
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 5 88 353 117 views
3 votes
1 answer
6
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 5 88 353 133 views
1 vote
1 answer
7
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 5 88 353 137 views
1 vote
1 answer
8
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 5 88 353 114 views
2 votes
1 answer
9
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 5 88 353 97 views
1 vote
1 answer
10
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 5 88 353 110 views
1 vote
1 answer
11
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 5 88 353 115 views
1 vote
1 answer
12
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 5 88 353 104 views
1 vote
1 answer
13
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 119 744 834 198 views
0 votes
1 answer
14
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 119 744 834 269 views
1 vote
1 answer
15
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 119 744 834 208 views
0 votes
1 answer
16
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 119 744 834 307 views
0 votes
1 answer
17
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 119 744 834 320 views
0 votes
1 answer
18
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 119 744 834 211 views
0 votes
0 answers
19
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 119 744 834 113 views
0 votes
1 answer
20
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 119 744 834 306 views
0 votes
0 answers
21
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 119 744 834 158 views
0 votes
1 answer
22
$₹6500/-$ 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 119 744 834 325 views
0 votes
1 answer
23
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 119 744 834 352 views
0 votes
1 answer
24
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 119 744 834 252 views
1 vote
2 answers
25
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 119 744 834 285 views
1 vote
1 answer
26
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 309 2254 2467 360 views
1 vote
1 answer
27
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 309 2254 2467 262 views
2 votes
1 answer
28
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 309 2254 2467 225 views
2 votes
1 answer
29
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 309 2254 2467 156 views
1 vote
1 answer
30
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 309 2254 2467 147 views
1 vote
1 answer
31
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 309 2254 2467 151 views
1 vote
1 answer
32
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 309 2254 2467 165 views
1 vote
1 answer
33
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 309 2254 2467 199 views
1 vote
1 answer
34
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 309 2254 2467 136 views
1 vote
1 answer
35
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 309 2254 2467 158 views
0 votes
1 answer
36
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 309 2254 2467 152 views
2 votes
1 answer
37
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 309 2254 2467 213 views
0 votes
0 answers
38
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 268 points 6 53 68 67 views
0 votes
0 answers
39
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 268 points 6 53 68 93 views
0 votes
0 answers
40
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 268 points 6 53 68 117 views
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