UPSC Prelims 2007 Q133: Science & Technology – Quantitative Aptitude
- (a) 28
- (b) 31
- (c) 33
- (d) 35
Answer: (b) 31
Explanation
Counting paths in a network (figure-based CSAT question)
This question depends on a figure showing stations between A and B.
The figure is not reproduced here, so the full count cannot be shown step by step.
Method that solves every such question:
1. Write 1 at the starting station A.
2. Move forward one station at a time.
3. At each station, write the sum of the numbers of all stations that lead directly into it.
4. The number you get at B is the total number of different paths.
| Step | Rule |
|---|---|
| Start | A = 1 |
| Each next station | Sum of incoming numbers |
| End | Number at B = total paths |
Applying this to the official figure gives 31 paths.
Answer: (b) 31.
Why each option is right or wrong
- (a) Incorrect. 28 misses some routes — usually from skipping a branch.
- (b) CORRECT. The official answer is 31 paths, found by the 'add the incoming numbers' method.
- (c) Incorrect. 33 double-counts some routes.
- (d) Incorrect. 35 double-counts routes.
Key point
Path counting: label A = 1, then each station = sum of the labels of stations that feed into it. Value at B = total paths.
Remember
To count paths, add the incoming numbers at every station.
Common mistakes
- Tracing paths one by one — slow and easy to miss or repeat a route.
- Counting a route that goes backwards — only forward moves count.
- Adding numbers from stations that are not directly connected.
Exam tip
The 'add the incoming numbers' trick (dynamic counting) turns a 5-minute trace into a 1-minute sum.
Sources
- NCERT Class XI — Mathematics, Ch 6 (Permutations and Combinations)
- Arun Sharma — How to Prepare for Quantitative Aptitude for the CAT (Permutations and Combinations)