Question

If $x$ and $y$ are integers, $7<y<16$, and $\frac{x}{y}=\frac{2}{5}$, how many possible values are there for $x$?

• A. One
• B. Two
• C. Three
• D. Four
• E. Five

Answer 1

The correct option is C Three

Given $x$ and $y$ are the integers.

$\frac{x}{y}=\frac{2}{5}$

$y=\frac{5x}{2}$

$7<y<16$

$7<\frac{5x}{2}<16$

$14<5x<32$ (multiplying by 2)

$\frac{14}{5}<x<\frac{32}{5}$ (dividing by 5)

$x\in \{3,4,5,6\}$