n is a whole number which, when divided by 4, leaves a remainder of 3. What will be the remainder when 2n is divided by 4?

Introduction / Context:
This problem uses basic modular arithmetic. We are told how a whole number n behaves when divided by 4 and then asked to predict the remainder when 2n is divided by 4. Instead of thinking of specific values for n, we can work with congruences and properties of remainders under multiplication.

Given Data / Assumptions:

- n is a whole number. - When n is divided by 4, the remainder is 3, that is n ≡ 3 (mod 4). - We must find the remainder when 2n is divided by 4.

Concept / Approach:
In modular arithmetic, if n leaves a remainder when divided by some modulus, then any multiple of n will also have a predictable remainder. Here, n ≡ 3 (mod 4), and we multiply both sides of this congruence by 2 to model 2n. This gives 2n ≡ 2 * 3 (mod 4). We then reduce 6 modulo 4 to find the required remainder.

Step-by-Step Solution:
Step 1: Translate the statement into a congruence: n ≡ 3 (mod 4). Step 2: Multiply both sides by 2 to represent 2n: 2n ≡ 2 * 3 (mod 4). Step 3: Compute 2 * 3 = 6. Step 4: Reduce 6 modulo 4. When 6 is divided by 4, the quotient is 1 and the remainder is 2. Step 5: Therefore, 6 ≡ 2 (mod 4), so 2n ≡ 2 (mod 4). Step 6: This means that when 2n is divided by 4, the remainder is 2.

Verification / Alternative check:
We can pick specific numbers for n that satisfy the given condition and test. For example, let n = 3. Then n divided by 4 leaves remainder 3. Compute 2n = 6, which divided by 4 leaves remainder 2. Another example is n = 7, since 7 divided by 4 leaves remainder 3. Then 2n = 14, and 14 divided by 4 leaves remainder 2 again. These examples confirm the general modular reasoning.

Why Other Options Are Wrong:
Option A (3) would suggest 2n ≡ 3 (mod 4), which contradicts the calculation 2 * 3 = 6 ≡ 2 (mod 4). Option C (1) and option D (0) do not match any consistent behavior of 2n for values of n congruent to 3 modulo 4. Checking sample values quickly reveals that 2n never leaves remainder 1 or 0 in this situation.

Common Pitfalls:
Some learners mistakenly double both the remainder and the modulus, which is incorrect. Others try to guess 2n by choosing a single example of n and may miscalculate the remainder. The correct approach is to use congruence rules systematically and reduce the product modulo 4.

Final Answer:
The remainder when 2n is divided by 4 is 2, which corresponds to option B.