Difficulty: Easy
Correct Answer: 60
Explanation:
Introduction / Context:This is another linear equation built from the difference of two fractional parts of a number. Solving requires careful fraction subtraction and then isolating the unknown. It checks comfort with least common multiples and proportional reasoning.
Given Data / Assumptions:
Concept / Approach:Subtract the fractions with a common denominator, then equate the result to 5 and solve for N. Using the identity (a/b − c/d) = (ad − bc) / bd helps to avoid errors.
Step-by-Step Solution:
Compute the difference: 3/4 − 2/3 = (9/12 − 8/12) = 1/12.Set the equation: (1/12) * N = 5.Solve: N = 5 * 12 = 60.Therefore, the required number is 60.Verification / Alternative check:Check: (3/4)*60 = 45; (2/3)*60 = 40; 45 − 40 = 5. The condition holds perfectly.
Why Other Options Are Wrong:48, 72, 84, and 36 yield differences other than 5 when substituted into the expression (3/4)N − (2/3)N.
Common Pitfalls:Computing 3/4 − 2/3 incorrectly (e.g., 1/12 reversed in sign) or multiplying by the wrong reciprocal when isolating N.
Final Answer:60
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