Three numbers in a 1:2:3 ratio have an H.C.F of 12. Find the numbers__________?
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Answer: D. 12, 24, 36
Explanation
Multiplying each term in the given ratio of 1 to 2 to 3 by the highest common factor of 12 scales the numbers. Performing the multiplication gives 1 times 12, 2 times 12, and 3 times 12 respectively. The resulting numbers are exactly 12, 24, and 36, which maintain the original ratio and common factor. The highest common factor of a set of numbers proportional to a given ratio is the multiplier for all terms. Ratios represent simplified forms of numbers where all original values have been divided by their common divisor. Reconstructing original numbers from a ratio requires multiplying each ratio component by the known common factor.
Option A uses a ratio of 1 to 2 to 3 but multiplies by an incorrect factor smaller than 12. Option B corresponds to a different ratio of 1 to 2 to 3 scaled by an incorrect common factor of 5. Option C uses larger numbers that share a common factor of 10 rather than the required factor of 12.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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