Question

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

• A. 34
• B. 33
• C. 32
• D. 35

Answer 1

The correct option is B 33

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