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

[fskilnik@GMATH]

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]

[fskilnik@GMATH]

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.