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

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fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

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

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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

Answer: [spoiler]____(C)__[/spoiler]

Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
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Source: Beat The GMAT — Problem Solving | Mon Feb 11, 2019 6:10 am

fskilnik@GMATH: GMAT Instructor; Posts: 1449; Joined: Sat Oct 09, 2010 2:16 pmFollowed by: 33 members; Thanked: 59 times

by fskilnik@GMATH » Tue Feb 12, 2019 4:59 am

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

Obs.: all angles are measured in degrees.

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

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

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)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16206; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Feb 12, 2019 7:39 am

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

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

Answer: C

Cheers,
Brent

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