Fraction Removal from a Number — Solve for the Original Value If three-fourths (3/4) of a number is subtracted from the number itself, the value obtained is 163. What is that original number?

Introduction / Context:This aptitude question translates a sentence about fractions into a simple linear equation. The expression “three-fourths of a number subtracted from the number” is a common prompt to test algebraic modeling and careful reading. Solving it requires only basic manipulation once the equation is set up correctly.

Given Data / Assumptions:

• The unknown number is positive and denoted by N.
• Subtracting 3/4 of N from N gives 163.
• We are to find the exact value of N.

Concept / Approach:The wording maps directly to the equation: N − (3/4)N = 163. Combine like terms on the left to isolate a single multiple of N, then solve by division. The structure highlights how fractional parts of a whole relate back to the whole number.

Step-by-Step Solution:Write the relation: N − (3/4)N = 163.Combine: (1 − 3/4)N = (1/4)N = 163.Solve for N: N = 163 * 4 = 652.Therefore, the original number is 652.

Verification / Alternative check:Compute 3/4 of 652 = 489. Then N − 3/4 N = 652 − 489 = 163, matching the given condition exactly.

Why Other Options Are Wrong:625, 562, 632, and 640 produce N − 3/4 N values of 156.25, 140.5, 158, and 160 respectively, none equal to 163.

Common Pitfalls:Misreading “three-fourths” as “three-four” or interpreting the phrase as (3/4N − N). Also, some candidates multiply 163 by 3 inadvertently instead of by 4.

Final Answer:652