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If 0 < x < 10...

Question

If $0 < x < 1000$ and $[\frac{x}{2}] + [\frac{x}{3}] + [\frac{x}{5}] = \frac{31}{30} x$ where [.] GIF; the number of possible values of x is

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Solution

LHS is integer
RHS must be integer for which x is multiple of 30
x=30, 60, 90, .........., 990
No. of possible values = 33

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