Number System

Quantitative Aptitude (RAS)

Title

45:30

8 of 24 completed

5 of 15 completed

38 of 100 completed

8 of 20 completed

Indian Economy - Understanding the basics of Indian economic system

If x., y z arc natural numbers , then the number of diftercnt soluti on s of the equation x + y + z = 6 are :

This questions was previously asked in

Complete-Test, Previous year (2018)

- We need to find how many different sets of natural numbers \((x, y, z)\) can sum up to 6.

- Natural numbers start from 1, so \(x, y, z\) must be at least 1.

- Rewrite the equation as \(x + y + z = 6\), where \(x, y, z > 0\).

- Method: Identify sets where each variable is greater than 0.

- Solution: Try different values for \(x\) and calculate possible corresponding \((y, z)\). Repeat for all possible values.

- The solutions are:

- \( (1,1,4), (1,2,3), (1,3,2), (1,4,1) \)

- \( (2,1,3), (2,2,2), (2,3,1) \)

- \( (3,1,2), (3,2,1) \)

- \( (4,1,1) \)

- Total solutions: 10

Correct Answer: Option: 3, 10