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

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
The graphs of y=7x+1 and y=kx^3 are represented in the figure shown  [#permalink]

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19 Feb 2019, 12:51
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Difficulty:

55% (hard)

Question Stats:

50% (02:08) correct 50% (02:38) wrong based on 24 sessions

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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

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: The graphs of y=7x+1 and y=kx^3 are represented in the figure shown  [#permalink]

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20 Feb 2019, 11:31
fskilnik 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

$$? = m$$

$$C = \left( {c,8} \right) \in {\rm{line}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = 7 \cdot c + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,c = 1$$

$$C = \left( {c,8} \right) = \left( {1,8} \right) \in {\rm{cubic}}\,\,\,\,\, \Rightarrow \,\,\,\,\,8 = k \cdot {1^3}\,\,\,\,\, \Rightarrow \,\,\,\,\,k = 8$$

$$A = \left( {0,n} \right) \in {\rm{line}}\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 7 \cdot 0 + 1\,\,\,\,\, \Rightarrow \,\,\,\,\,n = 1$$

$$B = \left( {m,n} \right) = \left( {m,1} \right) \in {\rm{cubic}}\,\,\,\,\,\mathop \Rightarrow \limits^{k\, = \,8} \,\,\,\,\,1 = 8 \cdot {m^3}$$

$$? = m = \root 3 \of {{1 \over 8}} = \root 3 \of {{{\left( {{1 \over 2}} \right)}^3}} = {1 \over 2}$$

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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: The graphs of y=7x+1 and y=kx^3 are represented in the figure shown  [#permalink]

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20 Feb 2019, 11:55
fskilnik 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

given
y=7x+1
and y=kx^3
value of coordinate C
y=7x+1
y=8
x=1 so C ( 1,8)
now
y=kx^3
8=k*1
k=8

so point A os
n=7*0+1
n=1 ; A ( 0,1)

also pt B
1=8 * x^3
x^3 = 1/8
x= 1/2
x= 0.5 IMO C
Re: The graphs of y=7x+1 and y=kx^3 are represented in the figure shown   [#permalink] 20 Feb 2019, 11:55
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