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

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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MathematicsFunctionsGeneral (Definition,type and special type)Medium2 minQB

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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

Answer:

Solution:

LHS is integer

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

$x = 30, 60, 90, \dots\dots, 990$

No. of possible values $= 33$

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

⏱ 2mℹ️ Source: QB

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