If a, b, and c are positive numbers such that a is b percent

[BTGmoderatorDC]

If a, b, and c are positive numbers such that a is b percent of c, what is the value of c?

(1) a is c percent of b.

(2) b is c percent of a.

OA B

Source: Manhattan Prep

[deloitte247]

$$a=b\%\ of\ c=\frac{b}{10}\cdot c$$
what is c ?
Statement 1
a is c percent of b
a is c% of b
$$\frac{c}{100}of\ b$$
value of c is still unknown
statement 1 is INSUFFICIENT.

Statement 2
b is c percent of a
$$b\ is\ c\%\ of\ a$$
$$\frac{c}{100}of\ a\ $$
$$a=\frac{b}{100}\cdot c$$
$$b=\frac{c}{100}\cdot\frac{b}{100}\cdot c$$
$$b=\frac{bc^2}{100^2}$$
$$\frac{100^2b}{b}=\frac{bc^2}{b}$$
$$\sqrt{c^2}=\sqrt{100^2}$$
$$c=100$$
Statement 2 alone is SUFFICIENT
$$answer\ is\ Option\ B$$