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Recent questions tagged numerical-answer

1 votes
1 answer
129
CAT 2019 Set-2 | Question: 70
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
How many pairs $(m,n)$ of positive integers satisfy the equation $m^{2}+105=n^{2}$ _______
4 votes
1 answer
133
CAT 2019 Set-2 | Question: 85
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
How many factors $2^{4}\times3^{5}\times10^{4}$ are perfect squares which are greater than $1$ _______
1 votes
1 answer
134
CAT 2019 Set-2 | Question: 91
John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his income from regular hours. Then, for how many hours did he work overtime _________
John gets Rs $57$ per hour of regular work and Rs $114$ per hour of overtime work. He works altogether $172$ hours and his income from overtime hours is $15\%$ of his inc...
1 votes
1 answer
135
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 _______
1 votes
1 answer
136
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 $1+2+3+\dots+n$ _______
1 votes
1 answer
138
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 $...
2 votes
1 answer
140
CAT 2018 Set-2 | Question: 69
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
The smallest integer $n$ such that $n^{3} - 11n^{2} + 32n - 28 >0$ is
2 votes
1 answer
143
CAT 2018 Set-2 | Question: 74
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________
Let $f\left (x \right ) = \max\left \{5x, 52 – 2x^{2}\right \}$ , where $x$ is any positive real numbers. Then the minimum possible value of $f(x)$ is ________
2 votes
1 answer
146
CAT 2018 Set-2 | Question: 77
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 > 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________
If $a$ and $b$ are integers such that $2x^{2}- ax + 2 0$ and $x^{2}-bx+8 \geq 0$ for all real numbers $x$, then the largest possible value of $2a-6b$ is _________
2 votes
1 answer
148
CAT 2018 Set-2 | Question: 80
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals
Let $t_{1}, t_{2},\dots$ be a real numbers such that $t_{1}+t_{2}+\dots+t_{n}=2n^{2}+9n+13$, for every positive integers $n\geq2$.If $t_{k}=103$ , then $k$ equals
2 votes
1 answer
149
CAT 2018 Set-2 | Question: 79
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest possible $x$ is _______
If $\text{N}$ and $x$ are positive integers such that $\text{N}^{\text{N}}=2^{160}$ and $\text{N}^{2} + 2^{\text{N}}$ is an integral multiple of $2^{x}$, then the largest...
2 votes
1 answer
150
CAT 2018 Set-2 | Question: 89
The arithmetic mean of $x,y$ and $z$ is $80$, and that of $x,y,z,u$ and $v$ is $75$, where $u=\left (x+y \right)/2$ and $v=\left (y+z \right)/2$. If $x\geq z$, then the minimum possible value of $x$ is ____________
The arithmetic mean of $x,y$ and $z$ is $80$, and that of $x,y,z,u$ and $v$ is $75$, where $u=\left (x+y \right)/2$ and $v=\left (y+z \right)/2$. If $x\geq z$, then the m...
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