In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Answer: A
Difficulty level: 650 - 700
Source: www.gmatprepnow.com
In the x-y coordinate plane, line k passes through
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Reminder (to my students) / Suggestion (to the general reader):Brent@GMATPrepNow wrote:In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Source: www.gmatprepnow.com
1. One property at a time, till the end. Then the other. ("Don´t let your brain dance!")
2. Start with the easier checking property (or the one you feel more comfortable).
Indifferent? Start with the first.
\[?\,\,\left( 1 \right)\,\,\,\,:\,\,\,\,\left( {5, - 4} \right)\,\,\mathop \in \limits^? \,\,\,{\text{line}}\,\,\]
\[\left( i \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{2}{5}\left( 5 \right) - 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\]
\[\left( {ii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{6}{5}\left( 5 \right) + 2\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\]
\[\left( {iii} \right)\,\,\, - 4\,\,\mathop = \limits^? \,\, - \frac{7}{{10}}\left( 5 \right) - \frac{3}{2}\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( C \right),\,\,\left( E \right)\]
\[?\,\,\left( 2 \right)\,\,\,\,:\,\,\,\,{\text{line}}\,\,x - {\text{intercept}}\,\,\,\mathop < \limits^? \,\,0\]
\[\left( i \right)\,\,0\, = \,\, - \frac{2}{5}\left( x \right) - 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( B \right)\]
\[\left( {ii} \right)\,\,0\, = \,\, - \frac{6}{5}\left( x \right) + 2\,\,\,\,\,\mathop \Rightarrow \limits^? \,\,\,x < \,\,0\,\,\,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{Refute}}\,\,\left( D \right)\]
The correct answer is (A).
This solution follows the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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Notice that, if the line passes through the origin, then the line has slope -4/5 (aka a slope of -0.8), but the line will not have a negative x-interceptBrent@GMATPrepNow wrote:In the x-y coordinate plane, line k passes through the point (5, -4) and has a negative x-intercept. Which of the following COULD be the equation of line k?
i) y = -0.4x - 2
ii) y = 2 - 1.2x
iii) y = -0.7x - 1.5
A) i only
B) ii only
C) iii only
D) i & ii only
E) i & iii only
Answer: A
Difficulty level: 650 - 700
Source: www.gmatprepnow.com
Notice that, if the line passes through the (0,4), then the line will have slope 0, BUT the line will not have a negative x-intercept. See below.
So, if the slope of the line is BETWEEN 0 and -0.8, then the line will have a negative x-intercept
Check the 3 statements:
i) y = -0.4x - 2
The slope = -0.4, which is BETWEEN 0 and -0.8. KEEP i for now
ii) y = 2 - 1.2x
Rewrite as: y = -1.2 + 2.
The slope = -1.2, which is NOT BETWEEN 0 and -0.8. So, ii cannot be true
iii) y = -0.7x - 1.5
The slope = -0.7, which is BETWEEN 0 and -0.8. KEEP iii for now
So far, i and iii COULD both be true.
However, in order for the point (5, -4) to be ON line k, its x and y coordinates must satisfy the equation of the line.
So, let's check i and iii
i) y = -0.4x - 2
Plug in x = 5 and y = -4 to get: -4 = -0.4(5) - 2 = -2 - 2 = -4
PERFECT!
So, i is true
iii) y = -0.7x - 1.5
Plug in x = 5 and y = -4 to get: -4 = -0.7(5) - 1.5 = -3.5 - 1.5 = -5
NO GOOD
So, iii is not true
Answer: A
Cheers,
Brent