Two numbers in a 1:4 ratio have an H.C.F of 84 and an L.C.M of 21. What is the larger number____________?
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Answer: C. 84
Explanation
Two numbers sharing a given ratio can be expressed with variables representing their proportional parts. The product of two numbers always equals the product of their highest common factor and least common multiple. Applying number properties to the given ratio and factors isolates the larger number as eighty-four. The product of any two positive integers equals the product of their HCF and LCM values. Ratios express the proportional relationship between two quantities using simplified integer terms. Solving ratio and factor problems requires combining fundamental arithmetic identities systematically.
Quantitative reasoning exams use number property puzzles to evaluate a candidate's analytical flexibility. Data analysts apply ratio relationships to scale datasets without distorting underlying proportions. Understanding HCF and LCM identities simplifies complex number theory equations significantly. Option A underestimates the number by confusing ratio terms with the final calculated value. Option B represents an intermediate proportional figure rather than the final solved number. Option D overestimates the value due to misapplied ratio scaling multipliers.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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