Question

What is the percentage of families in the city have telephones?
(I) $50\%$ of the families of the city have televisions.
(II) $30\%$ of the television owners of the city have telephones

• A. Statement (I) ALONE is sufficient, but statement (II) B alone is not sufficient
• B. Statement (II) ALONE is sufficient, but statement (I) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
• D. EACH statement ALONE is sufficient

Answer 1

The correct option is C BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient

Let total families in city = x
(I) $\Rightarrow$ Families having television $=\frac{x}{2}$
(II) $\Rightarrow$ Families having television $=30$ % of $\frac{x}{2}=\frac{3x}{20}$
$\therefore$ Required % $=\frac{3x/20}{x}\times 100$
Hence, both statements together are necessary to answer the question.