Question

A value z is multiplied by $\frac{1}{3},\frac{1}{2}$ is subtracted from the result, and the square root of the end result is $4$. What was the original number?

• A. $\frac{1}{2}$
• B. $5\frac{1}{6}$
• C. $15\frac{1}{2}$
• D. $16$
• E. $49\frac{1}{2}$

Answer 1

The correct option is E $49\frac{1}{2}$

According to the question,

$\sqrt{\frac{1}{3}z-\frac{1}{2}}=4$

Squaring both the sides, we get

$\frac{1}{3}z-\frac{1}{2}=16$

$\frac{1}{3}z=16+\frac{1}{2}$

$\frac{1}{3}z=\frac{32+1}{2}$

$\frac{1}{3}z=\frac{33}{2}$

$z=\frac{99}{2}$

$z=49\frac{1}{2}$