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Source: — Data Sufficiency |

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by ceilidh.erickson » Mon Apr 25, 2016 11:28 am
Does the line with the equation ax + by = c, where a, b, cand c are real constants, cross the x-axis?
(1) b ≠ 0
(2) ab > 0
The question is asking if this particular line crosses the x-axis. Try thinking about the opposite: the only lines that will never cross the x-axis are horizontal lines. Horizontal lines have a slope of 0.

Rephrased question: does the line have a non-zero slope?

First, rearrange the the equation into y = mx + b form:
y = (-ax)/b + c/b

Thus, the slope = -a/b
The only way for this slope to be 0 is is a = 0. So rephrase again:

Further rephrased question: Does the variable a represent a non-zero number?

(1) b ≠ 0

This tells us nothing about a. Insufficient.

(2) ab > 0

If the product of a and b is greater than 0, then a ≠ 0. Sufficient!

The answer is B.
Ceilidh Erickson
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Harvard Graduate School of Education
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by girishj » Mon Apr 25, 2016 6:19 pm
Thanks Ceilidh.
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by DavidG@VeritasPrep » Tue Apr 26, 2016 5:32 am
Does the line with the equation ax + by = c, where a, b, and c are real constants, cross the x-axis?
(1) b ≠ 0
(2) ab > 0
After you review Ceilidh's elegant solution, go back and ask yourself: how does the answer change if the question had asked if the line crosses the y-axis?
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by Neilsheth2 » Fri May 20, 2016 5:36 pm
DavidG@VeritasPrep wrote:
Does the line with the equation ax + by = c, where a, b, and c are real constants, cross the x-axis?
(1) b ≠ 0
(2) ab > 0
After you review Ceilidh's elegant solution, go back and ask yourself: how does the answer change if the question had asked if the line crosses the y-axis?
Hey correct me if I am wrong so now the question rephrased would be whether the slope is undefined? That can be only done if the denominator is 0.
A- states it cant be 0 so SUFF
b- states that the slope is some number so again SUFF

Therefore D.
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by DavidG@VeritasPrep » Sat May 21, 2016 5:35 am
Neilsheth2 wrote:
DavidG@VeritasPrep wrote:
Does the line with the equation ax + by = c, where a, b, and c are real constants, cross the x-axis?
(1) b ≠ 0
(2) ab > 0
After you review Ceilidh's elegant solution, go back and ask yourself: how does the answer change if the question had asked if the line crosses the y-axis?
Hey correct me if I am wrong so now the question rephrased would be whether the slope is undefined? That can be only done if the denominator is 0.
A- states it cant be 0 so SUFF
b- states that the slope is some number so again SUFF

Therefore D.
Exactly :)
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