Question : Let $x$ be the least number of 4 digits that when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2000 and 2500, then what is the sum of the digits of $x$?

Option 1: 4

Option 2: 15

Option 3: 9

Option 4: 10

Question : Let $x$ be the least number which when divided by 8, 9, 12, 14 and 36 leaves a remainder of 4 in each case, but $x$ is divisible by 11. The sum of the digits of $x$ is

Option 1: 5

Option 2: 6

Option 3: 9

Option 4: 4

Question : What is the smallest perfect square number that is completely divisible by 4, 6, 9, 12, and 15?

Option 1: 784

Option 2: 900

Option 3: 961

Option 4: 841

Question : If the 9-digit number $72 x 8431y 4$ is divisible by 36, what is the value of $(\frac{x}{y}-\frac{y}{x})$ for the smallest possible value of $y$, given that $x$ and $y$ are natural numbers?

Option 1: $1 \frac{5}{7}$

Option 2: $2 \frac{1}{10}$

Option 3: $1 \frac{2}{5}$

Option 4: $2 \frac{9}{10}$

Question : Let $x$ be the least 4-digit number which when divided by 2, 3, 4, 5, 6 and 7 leaves a remainder of 1 in each case. If $x$ lies between 2800 and 3000, then what is the sum of the digits of $x$?

Option 1: 12

Option 2: 15

Option 3: 13

Option 4: 16