📘 Quiz

Solution: Step 1: The first condition states that when 'n' is divided by 4, the remainder is 3. This can be written in the form of n = (divisor * quotient) + remainder: n = 4q + 3, where q is a whole number (the quotient). Step 2: We need to find the remainder when 2n is divided by 4. Step 3: Multiply the expression for n by 2: 2n = 2 * (4q + 3) = 8q + 6. Step 4: Now, divide 8q + 6 by 4. To find the remainder, rewrite 8q + 6 such that it highlights multiples of 4: 8q + 6 = 8q + 4 + 2. Step 5: Factor out 4 from the terms that are multiples of 4: 8q + 4 + 2 = 4(2q + 1) + 2. Step 6: This expression shows that when 2n is divided by 4, the quotient is (2q + 1) and the remainder is 2. Step 7: Therefore, the remainder when 2n is divided by 4 is 2.