Fractions of a Number — Sum Exceeds the Number by 4 The sum of one-half, one-third, and one-fourth of a certain number exceeds the number itself by 4. Determine the number.

Introduction / Context:
This problem is a straightforward algebraic setup involving fractions of an unknown. The key is to carefully translate “sum exceeds the number by 4” into an equation and then solve for the unknown using common denominators. It is representative of quick-reasoning number system questions.

Given Data / Assumptions:

• Let the number be x.
• Sum of fractions: x/2 + x/3 + x/4.
• This sum is equal to x + 4.
• Find x and match with the options.

Concept / Approach:
Combine the fractions on the left using the common denominator 12. The coefficients become 6/12, 4/12, and 3/12, summing to 13/12. Then equate 13x/12 to x + 4 and solve. Finally, check whether the calculated value is present among the options; if not, select “None of these.”

Step-by-Step Solution:
Compute LHS: x/2 + x/3 + x/4 = (6x + 4x + 3x)/12 = 13x/12.Set equation: 13x/12 = x + 4.Subtract x: (13x/12 − x) = 4 → (x/12) = 4.Solve: x = 4 * 12 = 48.

Verification / Alternative check:
Plug back: 48/2 + 48/3 + 48/4 = 24 + 16 + 12 = 52; the number itself is 48; 52 exceeds 48 by 4. Condition satisfied.

Why Other Options Are Wrong:
24, 36, and 72 do not satisfy the equation; the correct value 48 is absent from the provided options, so “None of these” is correct.

Common Pitfalls:
Adding fractional coefficients incorrectly; setting “exceeds by 4” as equals 4 instead of equals x + 4; forgetting to scan choices for the exact computed value.

Final Answer:
None of these