Arun Sharma Solutions for Exercise 3: Level of Difficulty

The sum of its digits of a three digit number is $12$. If we subtract $495$ from the number consisting of the same digits written in reverse order, we shall get the required number. Find that three digit number if the sum all pairwise products of the digits constituting that number is $41$.

Suppose the sum of $\mathrm{n}$ consecutive integers is $x+\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+.....+\left(x+(n-1\right))=1000$, then which of the following cannot be true about the number of terms $n$

$N=202\times 20002\times 200000002\times 20000000000000002\times 20000000...2\left(31 \mathrm{zeroes}\right)$. The sum of digits in this multiplication will be

Twenty five sets of problems on Data Interpretation one each for the DI sections of $25$ CATALYST tests were prepared by the AMS research team. The DI section of each CATALYST contained $50$ questions of which exactly $35$ questions were unique, i.e. they had not been used in the DI section of any of the other $24$ CATALYSTS. What could be the maximum possible number of questions prepared for the DI sections of all the $25$ CATALYSTS put together?

In the above question, what could be the minimum possible number of questions prepared?

What is the maximum number of elements that one can pick from the set of natural numbers from $1$ to $20$ such that the product of no two of them results in a perfect square or perfect cube?

$abcdefghij$ is a ten-digit number with distinct digits such that $a > b > c, d > e > f, g > h > i > j$. $a, b, c$ are consecutive even digits and $g, h, i, j$ are consecutive odd digits.If $d + e + f = 9$, then what is the value of $\left[\frac{a \times b \times c \times d}{i}\right]$ where [ ] denotes greatest integer function?

$N = abc$ is a three digit number, the sum of whose digits is $\frac{1}{7}$th of the product of its digits. Then how many possible sets of $(a, b, c)$ are possible?

 ${\left(3132!\right)}_{10} = {\left(x\right)}_{34}$, then what will be the number of consecutive zeroes at the end of '$x$' ?