Given that $\frac{z}{2} = \frac{y}{x}$
In the equation above, the numbers $x, y$ and $z$ are either positive or negative. Which of the following must be equal to $4$ ?

2 x y

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2 z

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\frac{x z}{2 y}

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\frac{2 y}{x z}

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\frac{2 x z}{y}

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Solution

The correct option is C $\frac{2 x z}{y}$
As given $\frac{z}{2} = \frac{y}{x}$
$\Rightarrow x z = 2 y$
Multiplying both sides by $2$
$\Rightarrow 2 x z = 4 y$
On dividing both sides by $y$ , we get
$\Rightarrow \frac{2 x z}{y} = \frac{4 y}{y}$
$\Rightarrow \frac{2 x z}{y} = 4$
Hence, option E is correct.

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x + 2 y + z = 4

2 x + y + 2 z = 5

x - y + z = 1

x, y, z

A . P .

\frac{x + y}{2 y - x} + \frac{y + z}{2 y - z}

7 x + 6 y + 4 z = 122

4 x + 5 y + 3 z = 88

9 x + 2 y + z = 78

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