Given that, $\frac{x}{3} + \frac{y}{12} = z$
In the equation shown above, $x, y$ and $z$ are positive integers. Which of the following can't be a value of $y$ ?

4

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6

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8

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12

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20

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Solution

The correct option is B $6$
As given, $\frac{x}{3} + \frac{y}{12} = z$
Solve the equation for $y$ :
$\Rightarrow$ $\frac{y}{12} = z - \frac{x}{3}$
$\Rightarrow$ $y = 12 (z - \frac{x}{3})$
$\Rightarrow$ $y = 12 z - 4 x$
$\Rightarrow$ $y = 4 (3 z - x)$
Since, $z$ and $x$ are integer, $(3 z - x)$ is an integer.
So, $y$ is multiple of $4$ . As we can see only answer B is not a multiple of $4$ .
Hence, option B is correct, which is not a possible value of $y$ .

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Given that, x3+y12=zIn the equation shown above, x,y and z are positive integers. Which of the following can't be a value of y?

Given that, $\frac{x}{3} + \frac{y}{12} = z$
In the equation shown above, $x, y$ and $z$ are positive integers. Which of the following can't be a value of $y$ ?