NIMCET 2015 — Reasoning PYQ

Step 1: Divisibility Rule for 5

A number is divisible by $5$ if its last digit (unit digit) is either $0$ or $5$.

In the given set of digits $\{2,3,5,6,7,9\}$, only $5$ is available to make the number divisible by $5$.

Step 2: Filling the positions

We need to form a $3$-digit number: $\underline{\text{Hundred}}\underline{\text{Ten}}\underline{\text{Unit}}$

1. Unit Digit: This position must be filled by the digit $5$ to ensure divisibility.

   • Number of ways = $1$ (using digit $5$)

2. Hundred Digit: Since repetition is not allowed, we cannot use $5$ again. We have $5$ remaining digits available $\{2,3,6,7,9\}$.

   • Number of ways = $5$

3. Ten Digit: Now we have used two digits ($5$ and one other). Out of the original $6$ digits, $4$ remain.

   • Number of ways = $4$

Step 3: Calculate the total

Using the Fundamental Principle of Counting, we multiply the number of ways to fill each position:

Conclusion:

There are $20$ such $3$-digit numbers that can be formed.

Correct Option: (b) 20