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
Answer: [spoiler]____(C)__[/spoiler]
In the figure given, x = 3(y-z). What is the value of x?
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- fskilnik@GMATH
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- fskilnik@GMATH
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Obs.: all angles are measured in degrees.fskilnik@GMATH 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
$$x = 3\left( {y - z} \right)\,\,\,\,\,\left( * \right)$$
$$? = x$$
$$\left( {{\rm{Last}}\,\,{\rm{figure}}} \right)\,\,\,\,x + z = \left[ {180} \right] = \left( {60 - x} \right) + y\,\,\,\,\, \Rightarrow \,\,\,\,\,2x = y - z + 60\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,{x \over 3} + 60$$
$$2x - {x \over 3} = 60\,\,\,\,\,\mathop \Rightarrow \limits^{ \cdot \,3} \,\,\,\,\,6x - x = 3 \cdot 60\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = {{3 \cdot 6 \cdot 10} \over 5} = 36$$
The correct answer is therefore (C).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Since angles on a LINE add to 180°, . . .fskilnik@GMATH 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 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
Answer: C
Cheers,
Brent