Evaluate the missing divisor in a decimal expression: (17.28 ÷ ?) ÷ (3.6 × 0.2) = 200. Determine the exact value of ? and show the steps using basic arithmetic of decimals.

Introduction / Context:
This question tests decimal arithmetic and algebraic manipulation. You are given a compound expression with division and multiplication, and you must isolate the unknown divisor “?” so that the overall equality holds. Mastery of decimal operations and the correct order of operations is essential for quick problem solving in aptitude tests.

Given Data / Assumptions:

• (17.28 ÷ ?) ÷ (3.6 × 0.2) = 200
• All quantities are real numbers; standard operator precedence applies.
• Goal: solve for the unknown value ?.

Concept / Approach:
First simplify the constant product in the denominator. Then treat the remaining expression as a simple proportion. Rearranging the equation to isolate the term 17.28 ÷ ? allows solving for ? by cross-multiplication and basic division of decimals.

Step-by-Step Solution:
Compute 3.6 × 0.2 = 0.72.The equation becomes (17.28 ÷ ?) ÷ 0.72 = 200.So 17.28 ÷ ? = 200 × 0.72 = 144.Hence ? = 17.28 ÷ 144.Compute 17.28 ÷ 144 = 0.12 (since 1728/144 = 12 ⇒ 17.28/144 = 0.12).

Verification / Alternative check:
Plug ? = 0.12 back: 17.28 ÷ 0.12 = 144; 144 ÷ 0.72 = 200. The equality holds exactly, confirming the result.

Why Other Options Are Wrong:

• 120, 12, 1.20, 1.2: These values produce the wrong intermediate quotient 17.28 ÷ ? and therefore fail to give 200 after dividing by 0.72.

Common Pitfalls:
Mistaking the order of division and multiplication, or miscomputing 3.6 × 0.2. Another frequent slip is moving decimals incorrectly when dividing by 144.

Final Answer:
0.12