Recent questions tagged cat2007

Answer the following question based on the information given below:A health-drink company’s $\text{R & D}$ department is trying to make various diet formulations, which c...

A function $f(x) $ satisfies $f(1)=3600$ and $f(1)+f(2)+ \dots + f(n) = n^2 f(n)$, for all positive integers $n>1.$ What is the value of $f(9)?$$80$$240$$200$$100$$120$

Ten years ago, the ages of the members of a joint family of eight people added up to $231$ years. Three years later, one member died at the age of $60$ years and a child ...

Consider the set $S = \{2, 3, 4, \dots , 2n+1\} $ where $n$ is a positive integer larger than $2007.$ Define $\text{X}$ as the average of the odd integers in $S$ and $\te...

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$

Consider four digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?$3$$2$$4$$0$$1$

A quadratic function f(x) attains a maximum of $3$ at $x=1.$ The value of the function at $x=0$ is $1.$ What is the value of $f(x)$ at $x=10?$$-119$$-159$$-110$$-180$$-10...