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

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GMATH Teacher
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Joined: 12 Oct 2010
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In the figure given, x=3(y-z). What is the value of x?  [#permalink]

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12 Feb 2019, 05:05
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Difficulty:

25% (medium)

Question Stats:

75% (03:15) correct 25% (03:08) wrong based on 12 sessions

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GMATH practice exercise (Quant Class 1)

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

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

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)
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Re: In the figure given, x=3(y-z). What is the value of x?  [#permalink]

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12 Feb 2019, 05:21
1
X+Z = 180
Y+60-X = 180......(1)
X+Z = Y+60-X
2X+Z-Y = 60
Also, given X = 3Y-3Z
6Y-6Z+Z-Y = 60
Y-Z = 12
Y = 12+Z...........(2)
(2) IN (1) 72+Z-X = 180
Z-X = 108
X+Z = 180
2Z = 288
Z = 144, Then X = 36

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Re: In the figure given, x=3(y-z). What is the value of x?  [#permalink]

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12 Feb 2019, 07:52
Top Contributor
fskilnik wrote:
GMATH practice exercise (Quant Class 1)

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°, . . .

. . . we know that x + z = 180
Subtract x from both sides to get: z = 180 - x

Since angles in a CIRCLE add to 360°. . .

. . . 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

Cheers,
Brent
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Re: In the figure given, x=3(y-z). What is the value of x?  [#permalink]

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12 Feb 2019, 10:32
fskilnik wrote:
GMATH practice exercise (Quant Class 1)

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.

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

$$? = x$$

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

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

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

Regards,
Fabio.
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Re: In the figure given, x=3(y-z). What is the value of x?  [#permalink]

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12 Feb 2019, 13:03
fskilnik wrote:
GMATH practice exercise (Quant Class 1)

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

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

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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Re: In the figure given, x=3(y-z). What is the value of x?   [#permalink] 12 Feb 2019, 13:03
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