Question

Is $x^2:y^2=1$?
(1) $(y-x)(x+y)=40\%\text{of}60-120\%\text{of}20$
(2) $x<y$

• A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient
• B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient
• C. BOTH statements TOGETHER are sufficient, but NEITHER statement alone is sufficient
• D. Statements (1) and (2) TOGETHER are NOT sufficient

Answer 1

Answer: (A)

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient

(1) $\Rightarrow (y-x)(x+y)=24-24=0$
$\Rightarrow y^2-x^2=0\Rightarrow y^2=x^2\Rightarrow \frac{x^2}{y^2}=1$
Hence we can be answered the question using statement (1) alone.(2) $\Rightarrow x<y$.
This does not always imply that $x^2<y^2$
(Because for example -3 and 2, -3 < 2 but $3^2\nless 2^2)$
$\therefore$ If $x<y\Rightarrow$ either $x^2<y^2$ or $x^2>y^2$
$\therefore$ We can't be determined the answer.
Hence (2) is not sufficient to answer the question.