Question 118

A rod is cut into 3 equal parts. The resulting portions are then cut into 12, 18 and 32 equal parts, respectively. If each of the resulting portions have integer length, the minimum length of the rod is

Solution

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The rod is cut into 3 equal parts thus the length of the rod will be a multiple of 3.
Each part is then cut into $$12 = 2^2*3$$
$$18 = 2*3^2$$ and $$32 = 2^5$$ parts and thus, each part of rod has to be a multiple of $$2^5*3^2 = 288$$
Thus, the rod will be a multiple of $$288*3 = 864$$
Thus, the minimum length of the rod is 864 units.
Hence, option B is the correct answer.

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