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

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by fskilnik@GMATH » Mon Feb 11, 2019 6:10 am

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GMATH practice exercise (Quant Class 1)

Image

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

(A) 27
(B) 33
(C) 36
(D) 45
(E) 72

Answer: [spoiler]____(C)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by fskilnik@GMATH » Tue Feb 12, 2019 4:59 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 1)

Image

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

(A) 27
(B) 33
(C) 36
(D) 45
(E) 72
Obs.: all angles are measured in degrees.

Image

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

$$\left( {{\rm{Last}}\,\,{\rm{figure}}} \right)\,\,\,\,x + z = \left[ {180} \right] = \left( {60 - x} \right) + y\,\,\,\,\, \Rightarrow \,\,\,\,\,2x = y - z + 60\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{x \over 3} + 60$$
$$2x - {x \over 3} = 60\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,3} \,\,\,\,\,6x - x = 3 \cdot 60\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = {{3 \cdot 6 \cdot 10} \over 5} = 36$$


The correct answer is therefore (C).


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

Regards,
Fabio.
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by Brent@GMATPrepNow » Tue Feb 12, 2019 7:39 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 1)

Image

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

(A) 27
(B) 33
(C) 36
(D) 45
(E) 72
Since angles on a LINE add to 180°, . . .
Image
. . . we know that x + z = 180
Subtract x from both sides to get: z = 180 - x


Since angles in a CIRCLE add to 360°. . .
Image
. . . we know that 60 + (180 - x) + y = 360
Simplify left side: 240 - x + y = 360
Subtract 240 from both sides to get: -x + y = 120
Add x to both sides to get: y = 120 + x

GIVEN: x = 3(y - z)
Rewrite as: x = 3y - 3z
Replace y and z (with values from above) to get: x = 3(120 + x) - 3(180 - x)
Expand right side: x = 360 + 3x - 540 + 3x
Simplify: x = 6x - 180
Subtract 6x from both sides to get: -5x = -180
Solve: x = 36

Answer: C

Cheers,
Brent
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