Number System MCQs with Answers & Explanations

**Step 1:** Let the two-digit number be represented as $10x + y$, where x is the tens digit and y is the units digit.

**Step 1:** To form the smallest number, we should arrange the digits in ascending order: 0, 3, 5, 6.

Let the four consecutive numbers be $n, (n+1), (n+2),$ and $(n+3)$.

The question is asking for the count of prime numbers between 2 and 30. A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself.

- **Greatest six-digit number:** 999,999

**Step 1:** The smallest five-digit number is 10000.

We are looking for numbers that satisfy three conditions:

We use the algebraic identity: $(a^n - b^n)$ is always divisible by $(a-b)$ for any positive integer $n$.

**Step 1:** Divide 1739 by 11 to find the remainder.

We use the algebraic identity: for an odd integer $n$, the expression $(a^n + b^n)$ is always divisible by $(a+b)$.

To solve this, we can factor out the smallest term, which is $3^{71}$, from the expression.

**Method 1: Using Algebra**

We need to find all the numbers between 1 and 100 that have a '2' in the tens digit position. These are the numbers in the twenties.

**Step 1:** The number of decimal places in a product is typically the sum of the decimal places of the numbers being multiplied.

According to the divisibility rule of 11, the difference between the sum of digits at odd places and the sum of digits at even places must be 0 or a multiple of 11.

We use the division algorithm formula:

**Step 1: Divisibility by 5.** For a number to be divisible by 5, its last digit (\$) must be either 0 or 5.

The divisibility rule for 9 states that the sum of the digits of a number must be divisible by 9.

We can find the remainder of each term when divided by 17 and then multiply the remainders.

**Step 1:** The greatest five-digit number is 99999.