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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsGeneral (Definition,type and special type)Medium2 minQB

MathematicsMediumsingle choice

If $0 < x < 1000$ and $[\frac{x}{2}] + [\frac{x}{3}] + [\frac{x}{5}] = \frac{31}{30} x$ , where [x] is the greatest integer less than or equal to x , the number of possible values of x is

Options:

Answer:

Solution:

∵ LHS is an integer

∴ RHS is must be an integer for which x is multiple of 30.

$∴ x = 30, 60, 90, 120, \dots .., 990$

⇒ Number of possible values of x is 33.

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:General (Definition,type and special type)

⏱ 2mℹ️ Source: QB

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