A number, when reduced by one-seventh of itself, gives a result equal to the sum of all the angles of a triangle in degrees. What is that number?

Introduction / Context:
This question combines basic fraction operations with a simple geometric fact: the sum of the interior angles of a triangle is 180 degrees. You are told that a number minus one seventh of itself equals 180, and you must find the number. This is a straightforward linear equation involving fractions and is common in quantitative aptitude tests.

Given Data / Assumptions:

• Let the required number be N.
• One seventh of N is N / 7.
• The number minus one seventh of itself equals 180.
• The sum of all angles of a triangle in degrees is 180.

Concept / Approach:
We translate the statement “a number when subtracted by one seventh of itself gives 180” into an algebraic equation: N − (1 / 7) * N = 180. Then we combine like terms on the left side and solve for N. This requires basic knowledge of fractions and how to factor and simplify linear expressions. Recognising the geometric fact about triangle angles just tells us that the result is 180, which is used in the equation.

Step-by-Step Solution:
Step 1: Let the number be N. Step 2: One seventh of N is N / 7. Step 3: According to the question, N − (N / 7) = 180. Step 4: Factor out N on the left side: N * (1 − 1 / 7) = 180. Step 5: Compute 1 − 1 / 7 = (7 / 7) − (1 / 7) = 6 / 7. Step 6: So we have N * (6 / 7) = 180. Multiply both sides by 7 / 6 to solve for N. Step 7: N = 180 * (7 / 6) = (180 / 6) * 7 = 30 * 7 = 210.

Verification / Alternative check:
Check the result by substituting N = 210 back into the original statement. One seventh of 210 is 210 / 7 = 30. Now compute N − N / 7 = 210 − 30 = 180. This matches the sum of the angles of a triangle, confirming that N = 210 is correct. No other option will satisfy this equation when tested in the same way.

Why Other Options Are Wrong:
Option 420: One seventh of 420 is 60, and 420 − 60 = 360, not 180.
Option 70: One seventh of 70 is 10, and 70 − 10 = 60, not 180.
Option 35: One seventh of 35 is 5, and 35 − 5 = 30, not 180.
Option 140: One seventh of 140 is 20, and 140 − 20 = 120, still not 180.

Common Pitfalls:
A common error is to interpret the statement as N − 1 / 7 = 180 instead of N − (1 / 7) * N = 180, which changes the equation completely. Another mistake is to mishandle fractions, especially when combining 1 − 1 / 7. Always express 1 as 7 / 7 when subtracting 1 / 7, and then solve the resulting simple equation. Verifying the answer by substitution is a good practice to confirm you did not make any fraction mistakes.

Final Answer:
The required number is 210.