Equation from Verbal Statement — “Dividing by 6 diminishes the number by 40” A number, when divided by 6, is diminished by 40 (i.e., the result is 40 less than the original number). Find the number.

Introduction / Context:
Translating words into equations is a frequent aptitude skill. The phrase “a number when divided by 6 is diminished by 40” means the quotient equals the original number minus 40. Setting up this equation unlocks the value immediately with basic algebra.

Given Data / Assumptions:

• Let the number be N.
• “Divided by 6” produces N/6.
• “Is diminished by 40” means equals N − 40.

Concept / Approach:
Form the equation N/6 = N − 40. Solve by clearing the denominator and isolating N. Always re-check by substituting back to ensure the verbal condition is satisfied exactly, avoiding misinterpretations of “diminished by.”

Step-by-Step Solution:
Set N/6 = N − 40.Multiply both sides by 6: N = 6N − 240.Rearrange: 5N = 240 → N = 240/5 = 48.Hence, the number is 48.

Verification / Alternative check:
Compute N/6 = 48/6 = 8 and N − 40 = 48 − 40 = 8. The two sides match precisely, confirming N = 48.

Why Other Options Are Wrong:
72, 84, 60, and 96 produce quotients and differences that do not match under the stated relationship.

Common Pitfalls:
Misreading the sentence as “N divided by 6 is 40 less than 6” (nonsense) or as “N divided by 6 equals 40,” which would give N = 240 but ignores “less than the original number.”

Final Answer:
48