A chocolate bar has 12 equal pieces. Manju gives 1/4 of the bar to Anju, 1/3 of the bar to Sujata, and 1/6 of the bar to Fiza. How many pieces of chocolate are left with Manju?

Introduction / Context:
This problem combines fraction operations with a concrete total number of items. By summing the fractional parts given away and applying the result to the total piece count, we can quickly compute the remaining pieces.

Given Data / Assumptions:

• Total pieces = 12.
• Given away: 1/4 + 1/3 + 1/6 of the entire bar.
• All pieces are equal and divisible according to the stated fractions.

Concept / Approach:
First, sum the fractions to find the total fraction given. Then, subtract from 1 to find the remaining fraction. Finally, multiply the remaining fraction by 12 to get the number of pieces left. Using a common denominator streamlines the addition.

Step-by-Step Solution:

Verification / Alternative check:
Compute given pieces directly: 1/4 of 12 = 3, 1/3 of 12 = 4, 1/6 of 12 = 2. Total given = 3 + 4 + 2 = 9. Leftover = 12 − 9 = 3. Matches the fraction method.

Why Other Options Are Wrong:
1, 2, 4, and 5 do not match the leftover count when the fractions are correctly applied to 12.

Common Pitfalls:
Adding denominators directly or using an incorrect common denominator; misreading the question as adding fractional pieces rather than fractions of the whole bar.

Final Answer:
3