Recent questions tagged arithmetic-progression

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CAT 2021 Set-2 | Quantitative Aptitude | Question: 10
Three positive integers $x,y$ and $z$ are in arithmetic progression. If $y – x > 2$ and $xyz = 5(x+y+z),$ then $z-x$ equals $12$ $8$ $14$ $10$

Three positive integers $x,y$ and $z$ are in arithmetic progression. If $y – x > 2$ and $xyz = 5(x+y+z),$ then $z-x$ equals $12$ $8$ $14$ $10$

asked Jan 20 in Quantitative Aptitude soujanyareddy13 2.7k points 70 views

1 vote

1 answer

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CAT 2019 Set-2 | Question: 96
If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$ _______

If $(2n+1)+(2n+3)+(2n+5)+\dots+(2n+47)=5280,$ then what is the value of $1+2+3+\dots+n$ _______

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

1 vote

1 answer

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CAT 2019 Set-2 | Question: 99
The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is $18$ $19$ $21$ $20$

The number of common terms in the two sequences: $15, 19, 23, 27,\dots,415$ and $14, 19, 24, 29,\dots,464$ is $18$ $19$ $21$ $20$

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 218 views

3 votes

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CAT 2018 Set-2 | Question: 67
The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is $80707$ $80773$ $80730$ $80751$

The value of the sum $7 \times 11 + 11 \times 15 + 15 \times 19 + \dots$ + $95 \times 99$ is $80707$ $80773$ $80730$ $80751$

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 214 views

2 votes

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CAT 2018 Set-2 | Question: 87
Let $a_{1},a_{2},\dots , a_{52}$ be a positive integers such that $a_{1}<a_{2}<\dots < a_{52}$. Suppose, their arithmetic mean is one less than the arithmetic mean of $a_{2},a_{3},\dots , a_{52}$. If $a_{52}=100$ , then the largest possible value of $a_{1}$ is ________ $20$ $23$ $48$ $45$

Let $a_{1},a_{2},\dots , a_{52}$ be a positive integers such that $a_{1}<a_{2}<\dots < a_{52}$. Suppose, their arithmetic mean is one less than the arithmetic mean of $a_{2},a_{3},\dots , a_{52}$. If $a_{52}=100$ , then the largest possible value of $a_{1}$ is ________ $20$ $23$ $48$ $45$

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 214 views

2 votes

1 answer

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CAT 2018 Set-1 | Question: 67
Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ratio of the geometric progression is $3/6$ $3/2$ $5/2$ $1/6$

Let $x, y, z$ be three positive real numbers in a geometric progression such that $x < y < z$. If $5x$, $16y$, and $12z$ are in an arithmetic progression then the common ratio of the geometric progression is $3/6$ $3/2$ $5/2$ $1/6$

asked Mar 20, 2020 in Quantitative Aptitude go_editor 13.3k points 152 views

1 vote

1 answer

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CAT 2017 Set-2 | Question: 92
If $\log\left ( 2^{a} \times 3^{b}\times 5^{c}\right )$ is the arithmetic mean of $\log\left ( 2^{2} \times 3^{3}\times 5 \right ),$ $\log\left ( 2^{6} \times3\times 5^{7} \right ),$ and $\log\left ( 2 \times3^{2}\times 5^{4} \right ),$ then $a$ equals $2$ None of these $6$ $7$

If $\log\left ( 2^{a} \times 3^{b}\times 5^{c}\right )$ is the arithmetic mean of $\log\left ( 2^{2} \times 3^{3}\times 5 \right ),$ $\log\left ( 2^{6} \times3\times 5^{7} \right ),$ and $\log\left ( 2 \times3^{2}\times 5^{4} \right ),$ then $a$ equals $2$ None of these $6$ $7$

asked Mar 16, 2020 in Quantitative Aptitude go_editor 13.3k points 155 views

1 vote

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CAT 2017 Set-1 | Question: 97
If the square of the $7^{\text{th}}$ term of an arithmetic progression with positive common difference equals the products of the $3^{\text{rd}}$ and $17^{\text{th}}$ terms, then the ratio of the first term to the common difference is $2:3$ $3:2$ $3:4$ $4:3$

If the square of the $7^{\text{th}}$ term of an arithmetic progression with positive common difference equals the products of the $3^{\text{rd}}$ and $17^{\text{th}}$ terms, then the ratio of the first term to the common difference is $2:3$ $3:2$ $3:4$ $4:3$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 159 views

1 vote

1 answer

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CAT 2017 Set-1 | Question: 100
Let $a_{1}, a_{2},\ldots, a_{3n}$ be an arithmetic progression with $a_{1} = 3$ and $a_{2}=7$. If $a_{1}+ a_{2}+\ldots +a_{3n}=1830$, then what is the smallest positive integer $m$ such that $m(a_{1}+ a_{2}+ \ldots + a_{n})>1830$? $8$ $9$ $10$ $11$

Let $a_{1}, a_{2},\ldots, a_{3n}$ be an arithmetic progression with $a_{1} = 3$ and $a_{2}=7$. If $a_{1}+ a_{2}+\ldots +a_{3n}=1830$, then what is the smallest positive integer $m$ such that $m(a_{1}+ a_{2}+ \ldots + a_{n})>1830$? $8$ $9$ $10$ $11$

asked Mar 13, 2020 in Quantitative Aptitude go_editor 13.3k points 182 views

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CAT 2016 | Question: 94
A series $\text{S1}$ of five positive integers is such that the third term is half the first term and the fifth term is $20$ more than the first term. In series $\text{S2},$ the nth term defined as the difference between the $(n+1)$ ... progression with a common difference of $30$. Second term of $\text{S2}$ is $50$ $60$ $70$ $\text{None of these}$

A series $\text{S1}$ of five positive integers is such that the third term is half the first term and the fifth term is $20$ more than the first term. In series $\text{S2},$ the nth term defined as the difference between the $(n+1)$ term and the $n^{\text{th}}$ ... is an arithmetic progression with a common difference of $30$. Second term of $\text{S2}$ is $50$ $60$ $70$ $\text{None of these}$

asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 189 views

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CAT 2016 | Question: 95
A series $\text{S1}$ of five positive integers is such that the third term is half the first term and the fifth term is $20$ more than the first term. In series $\text{S2}$, the $n$th term defined as the difference between the $(n+1)$ ... difference of $30$. What is the average value of the terms of series $\text{S1}$? $60$ $70$ $80$ Average is not an integer

A series $\text{S1}$ of five positive integers is such that the third term is half the first term and the fifth term is $20$ more than the first term. In series $\text{S2}$, the $n$th term defined as the difference between the $(n+1)$ term and the $n^{\text{th}}$ ... a common difference of $30$. What is the average value of the terms of series $\text{S1}$? $60$ $70$ $80$ Average is not an integer

asked Mar 11, 2020 in Quantitative Aptitude go_editor 13.3k points 93 views

1 vote

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CAT 2015 | Question: 86
Fourth term of an arithmetic progression is $8$. What is the sum of the first $7$ terms of the arithmetic progression? $7$ $64$ $56$ Cannot be determined

Fourth term of an arithmetic progression is $8$. What is the sum of the first $7$ terms of the arithmetic progression? $7$ $64$ $56$ Cannot be determined

asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 177 views

0 votes

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CAT 2015 | Question: 94
Consider the set $\text{S} = \left \{ 1, 2, 3, \dots,1000 \right \}$. How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and end with $1000$ and have at least $3$ elements? $3$ $4$ $6$ $7$

Consider the set $\text{S} = \left \{ 1, 2, 3, \dots,1000 \right \}$. How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and end with $1000$ and have at least $3$ elements? $3$ $4$ $6$ $7$

asked Mar 9, 2020 in Quantitative Aptitude go_editor 13.3k points 115 views

2 votes

1 answer

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CAT 2019 Set-1 | Question: 75
If $a_{1},a_{2}\dots$ are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\dots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n-1}}}$ $\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}$ $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$ $\frac{n}{\sqrt{a_{1}}-\sqrt{a_{n+1}}}$

If $a_{1},a_{2}\dots$ are in A.P., then, $\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\dots+\frac{1}{\sqrt{a_{n}}+\sqrt{a_{n+1}}}$ is equal to $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n-1}}}$ $\frac{n}{\sqrt{a_{1}}+\sqrt{a_{n+1}}}$ $\frac{n-1}{\sqrt{a_{1}}+\sqrt{a_{n}}}$ $\frac{n}{\sqrt{a_{1}}-\sqrt{a_{n+1}}}$

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

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CAT 2003 | Question: 1-140
if $\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to $5$ $4$ $2$ $3$

if $\log_3\left(2^x - 5\right), \: \log_3\left(2^x - \frac{7}{2}\right)$ are in arithmetic progression, then the value of $x$ is equal to $5$ $4$ $2$ $3$

asked Feb 10, 2016 in Quantitative Aptitude go_editor 13.3k points 313 views

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16

CAT 2003 | Question: 1-110
The sum of $3$-rd and $15$-th elements of an arithmetic progression is equal to the sum of $6$-th, $11$-th and $13$-th elements of the same progression. Then which element of the series should necessarily be equal to zero? $1$-st $9$-th $12$-th None of these

The sum of $3$-rd and $15$-th elements of an arithmetic progression is equal to the sum of $6$-th, $11$-th and $13$-th elements of the same progression. Then which element of the series should necessarily be equal to zero? $1$-st $9$-th $12$-th None of these

asked Feb 5, 2016 in Quantitative Aptitude go_editor 13.3k points 406 views

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CAT 2004 | Question: 43
If the sum of first $11$ terms of an arithmetic progression equals that of a first $19$ terms, then what is the sum of the first $30$ terms? $0$ $-1$ $1$ Not unique

If the sum of first $11$ terms of an arithmetic progression equals that of a first $19$ terms, then what is the sum of the first $30$ terms? $0$ $-1$ $1$ Not unique

asked Jan 12, 2016 in Quantitative Aptitude go_editor 13.3k points 296 views

0 votes

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CAT 2006 | Question: 62
Consider the set $\text{S} = \{1, 2, 3, \dots, 1000\}.$ How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and with $1000$ and have at least $3$ elements? $3$ $4$ $6$ $7$ $8$

Consider the set $\text{S} = \{1, 2, 3, \dots, 1000\}.$ How many arithmetic progressions can be formed from the elements of $\text{S}$ that start with $1$ and with $1000$ and have at least $3$ elements? $3$ $4$ $6$ $7$ $8$

asked Dec 28, 2015 in Quantitative Aptitude go_editor 13.3k points 133 views

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