Question

Which of the following statements are true?

A. If $x : y = 3 : 1$ , then $x^3 - y^3 = \frac{10}{11}$ B. If $x = y + 12$ , $x : y = 3 : 2$ and $z : y = 1 : 3$ , then $z + x = 44$ C. If $3x = 8y$ and $5y = 9z$ , then $\frac{x}{z} = \frac{72}{15}$

Choose the most appropriate answer from the options given below:

Accepted Answer

C. A. $x : y = 3 : 1 \Rightarrow x = 3k, y = k$. $x^3 - y^3 = 27k^3 - k^3 = 26k^3$, which depends on $k$ and cannot be determined as $\frac{10}{11}$. False. B. $x : y = 3 : 2 \Rightarrow 3k - 2k = 12 \Rightarrow k = 12$. So $x = 36, y = 24$. Since $z : y = 1 : 3$, $z = 8$. $z + x = 8 + 36 = 44$. True. C. $3x = 8y \Rightarrow \frac{x}{y} = \frac{8}{3}$ and $5y = 9z \Rightarrow \frac{y}{z} = \frac{9}{5}$. $$\frac{x}{z} = \frac{x}{y} 	imes \frac{y}{z} = \frac{8}{3} 	imes \frac{9}{5} = \frac{24}{5} = \frac{72}{15}$$ True. Thus, statements B and C are correct.

Verifying Algebraic and Ratio Statements

Explanation

Practise this under exam conditions