In the figure given, x=3(y-z). What is the value of x?

Obs.: all angles are measured in degrees.



\(x = 3\left( {y - z} \right)\,\,\,\,\,\left( * \right)\)

\(? = x\)

\(\left( {{\rm{Last}}\,\,{\rm{figure}}} \right)\,\,\,\,x + z\,\, = \,\,\left[ {180} \right]\,\, = \,\,\left( {60 - x} \right) + y\,\,\,\,\, \Rightarrow \,\,\,\,\,2x = y - z + 60\,\,\,\,\mathop = \limits^{\left( * \right)} \,\,\,\,{x \over 3} + 60\)

\(2x - {x \over 3} = 60\,\,\,\,\mathop \Rightarrow \limits^{ \cdot {\mkern 1mu} 3} \,\,\,\,6x - x = 3 \cdot 60\,\,\,\, \Rightarrow \,\,\,\,? = {{3 \cdot 6 \cdot 10} \over 5} = 36\)


The correct answer is (C).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.

We have been told:
i) x = 3 ( y - z ) => x = 3y - 3z

From the figure we can see:

ii) x + z = 180
iii) y + z + 60 = 360 => y + z = 300

from i) & iii) we get:
iv) 180 - z = 3y - 3z => 3y - 2z = 180

from ii) & iii) we get:
3y + 3z = 900
-3y + 2z = - 180
=> 5z = 720 => z = 144

then from ii) we get: x = 36

Hence C is the correct answer.

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