A number exceeds one sixth of itself by 30. What is the value of this number?

Introduction / Context:
This question is a simple algebra problem involving fractions of a number. It asks you to express the relationship between a number and one sixth of that number, and then solve for the original number given the difference. This is common in aptitude tests and reinforces the idea of translating words into equations.

Given Data / Assumptions:

- Let the unknown number be N.

- The number N exceeds one sixth of itself by 30.

- In symbols: N is greater than N / 6 by 30.

Concept / Approach:
We convert the sentence into an algebraic equation. The phrase “exceeds its 1/6 by 30” means N - (N / 6) = 30. Once we have this equation, we can solve for N by simple manipulation. The key idea is understanding that the difference between a number and a fraction of itself can be written as a single multiple of the number.

Step-by-Step Solution:
Step 1: Let the number be N. Step 2: Translate the description into an equation. N - N / 6 = 30. Step 3: Combine like terms on the left side. N - N / 6 = (6N / 6) - (N / 6) = 5N / 6. So we get 5N / 6 = 30. Step 4: Solve for N. Multiply both sides by 6: 5N = 30 * 6 = 180. Now divide by 5: N = 180 / 5 = 36.

Verification / Alternative check:
Compute one sixth of 36: 36 / 6 = 6. Now check the condition: 36 exceeds 6 by 30 because 36 - 6 = 30. So N = 36 satisfies the given statement perfectly.

Why Other Options Are Wrong:
- 120: One sixth is 20; 120 - 20 = 100, not 30.
- 150: One sixth is 25; 150 - 25 = 125, not 30.
- 24: One sixth is 4; 24 - 4 = 20, not 30.

Common Pitfalls:
A common mistake is to set up the equation as N / 6 - N = 30 or N + N / 6 = 30, which reverses the intended relationship. Another typical error is mishandling the fraction when combining terms or solving the resulting equation. Writing the fraction with a common denominator helps avoid these errors.

Final Answer:
The required number is 36.