The graphs of y=7x+1 and y=kx^3 are represented in the figur

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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 » Tue Feb 19, 2019 11:47 am

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GMATH practice exercise (Quant Class 13)

The graphs of y=7x+1 and y=kx^3 are represented in the figure shown (k is a constant). If line AB is parallel to the x-axis, what is the abscissa (x-coordinate) of point B?

(A) 1
(B) 0.75
(C) 0.5
(D) 0.25
(E) 0.125

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 | Tue Feb 19, 2019 11:47 am

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

by fskilnik@GMATH » Wed Feb 20, 2019 10:20 am

fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 13)

The graphs of y=7x+1 and y=kx^3 are represented in the figure shown (k is a constant). If line AB is parallel to the x-axis, what is the abscissa (x-coordinate) of point B?

(A) 1
(B) 0.75
(C) 0.5
(D) 0.25
(E) 0.125

$$? = m$$
$$C = \left( {c,8} \right) \in {\rm{line}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = 7 \cdot c + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 1$$
$$C = \left( {c,8} \right) = \left( {1,8} \right) \in {\rm{cubic}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = k \cdot {1^3}\,\,\,\,\, \Rightarrow \,\,\,\,\,k = 8$$
$$A = \left( {0,n} \right) \in {\rm{line}}\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 7 \cdot 0 + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 1$$
$$B = \left( {m,n} \right) = \left( {m,1} \right) \in {\rm{cubic}}\,\,\,\,\,\mathop \Rightarrow \limits^{k\, = \,8} \,\,\,\,\,1 = 8 \cdot {m^3}$$
$$? = m = \root 3 \of {{1 \over 8}} = \root 3 \of {{{\left( {{1 \over 2}} \right)}^3}} = {1 \over 2}$$

The correct answer is (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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