Question

The number of ordered pair $(x,y)$ satisfying the equation $\left[\frac{x}{2}\right]+\left[\frac{2x}{3}\right]+\left[\frac{y}{4}\right]+\left[\frac{4y}{5}\right]=\frac{7x}{6}+\frac{21}{20}y$ where $0<x,y<30$ and $\left[\right]$ denotes greatest integer function is equal to

• A. $5$
• B. $1$
• C. $4$
• D. $3$

Answer 1

Answer: (C)

$4$

It is given that $0<x,y<30$.
Now for x to be divisible by 2 and 3, it has to be a multiple of 6.
Hence
$x=6,12,18,24$ ...(i) since $0<x<30$.
And for y to be divisible by both 4 and 5, it has to be a multiple of 20.
Hence
$y=20$ ...(ii) since $0<y<30$
Hence we get the ordered pairs as
$(6,20),(12,20),(18,20),(24,20)$.
Hence 4 ordered pairs.