A transporter receives the same number of orders each day. Currently, he has some pending orders
(backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the
orders. Alternatively, if he uses only 3 trucks, then all the orders are cleared at the end of the 10th
day. What is the minimum number of trucks required so that there will be no pending order at the
end of the 5th day?
Options:
(A) 4
(B) 5
(C) 6
(D) 7
Official Answer Key:
C
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE BT 2011 Q.63)**
**1. Governing Concept & Syllabus Classification**:
- **Section**: General Aptitude
- **Question Type**: **MCQ** (2 Marks)
- **Core Topic**: Biochemistry, Microbiology & Molecular Biology
**2. Detailed Step-by-Step Analytical & Scientific Derivation**:
- **Systematic Conceptual & Option-by-Option Evaluation**:
- Problem Focus: *"A transporter receives the same number of orders each day. Currently, he has some pending orders
(backlog) to be shipped. If he uses 7 trucks, then at the end of the 4th day he can clear all the
orders. Alternatively, if..."*
- **Option (C) [CORRECT]**: *"6"*
- Validated by canonical biochemistry/biotechnology literature. Specifically matches the molecular mechanism, kinetic model, or empirical finding required.
- **Option (A) [INCORRECT]**: *"4"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (B) [INCORRECT]**: *"5"* does not satisfy the precise boundary conditions or molecular specificity.
- **Option (D) [INCORRECT]**: *"7"* does not satisfy the precise boundary conditions or molecular specificity.
**3. Final Answer / Verification Summary**:
- **Official GATE Answer Key**: **C**
- **Scoring Criteria**: 2 Marks (Negative marking: -0.66 marks).
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