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16 Sep 2014, 01:03
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If \(abc \ne 0\), is the x-intercept of the line \(ax + by + c = 0\) negative?
(1) \(ba \lt 0\).
(2) \(ac \gt 0\).
(1) \(ba \lt 0\).
(2) \(ac \gt 0\).
16 Sep 2014, 01:03
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Official Solution:
If \(abc \ne 0\), is the x-intercept of the line \(ax + by + c = 0\) negative?
The x-intercept of a line is the value of \(x\) when \(y=0\). For the line \(ax+by+c=0\), the x-intercept is given by \(x=-\frac{c}{a}\). The question essentially asks: Is \(-\frac{c}{a} < 0\)? Which can be rephrased as: Is \(\frac{c}{a} > 0\)? This boils down to whether \(c\) and \(a\) have the same sign.
(1) \(ba \lt 0\).
This is not sufficient as it doesn't tell us if \(c\) and \(a\) have the same sign.
(2) \(ac \gt 0\).
From this statement, it's clear that \(c\) and \(a\) have the same sign. Hence, it's sufficient.
Answer: B
If \(abc \ne 0\), is the x-intercept of the line \(ax + by + c = 0\) negative?
The x-intercept of a line is the value of \(x\) when \(y=0\). For the line \(ax+by+c=0\), the x-intercept is given by \(x=-\frac{c}{a}\). The question essentially asks: Is \(-\frac{c}{a} < 0\)? Which can be rephrased as: Is \(\frac{c}{a} > 0\)? This boils down to whether \(c\) and \(a\) have the same sign.
(1) \(ba \lt 0\).
This is not sufficient as it doesn't tell us if \(c\) and \(a\) have the same sign.
(2) \(ac \gt 0\).
From this statement, it's clear that \(c\) and \(a\) have the same sign. Hence, it's sufficient.
Answer: B
22 Jun 2018, 11:54
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I think this is a high-quality question and I agree with explanation.
