[GMAT math practice question]
In the coordinate plane, is the x-intercept of the line ax + by + c = 0 less than 0?
1) ac > 0
2) bc > 0
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In the coordinate plane, is the x-intercept of the line ax +
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Max@Math Revolution
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Target question: Is the x-intercept less than 0?Max@Math Revolution wrote: In the coordinate plane, is the x-intercept of the line ax + by + c = 0 less than 0?
1) ac > 0
2) bc > 0
This is a good candidate for rephrasing the target question.
Aside: Here's a video with tips on rephrasing the target question: https://www.gmatprepnow.com/module/gmat- ... cy?id=1100
The x-intercept is the point where a line crosses the x-axis. At this point, the y-coordinate is ZERO
So, the x-intercept is the value of the x-coordinate when y = 0
Now take the equation of the line and replace y with 0 to get: ax + b(0) + c = 0
Solve for x
Simplify: ax + c = 0
So: ax = -c
So: x = -c/a
This means the x-intercept = -c/a
We can now REPHRASE the target question....
REPHRASED target question: Is -c/a less than 0?
Statement 1: ac > 0
If the product ac is positive, then EITHER a and c are both positive OR a and c are both negative
In both cases, c/a is positive, which means -c/a must be NEGATIVE
So, the answer to the REPHRASED target question is YES, -c/a IS less than 0
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT
Statement 2: bc > 0
Since we aren't given any information about a, there's no way to determine whether -c/a is less than 0 or greater than 0
Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
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Brent Hanneson - Creator of GMATPrepNow.com
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Max@Math Revolution
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=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
We need to plug in 0 for y to get the x-intercept. This yields ax +b*0 + c = 0, or ax + c = 0.
The x-intercept is -c/a and the question asks if -c/a < 0.
Now,
-c/a < 0
=> c/a > 0
=> ac > 0.
Thus, condition 1) is sufficient.
Condition 2)
If a = 1, b = 1 and c = 1, then the x-intercept -c/a = -1 is less than 0.
If a = -1, b = 1 and c = 1, then the x-intercept -c/a = 1 is greater than 0.
Since we don't have a unique solution, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.
We need to plug in 0 for y to get the x-intercept. This yields ax +b*0 + c = 0, or ax + c = 0.
The x-intercept is -c/a and the question asks if -c/a < 0.
Now,
-c/a < 0
=> c/a > 0
=> ac > 0.
Thus, condition 1) is sufficient.
Condition 2)
If a = 1, b = 1 and c = 1, then the x-intercept -c/a = -1 is less than 0.
If a = -1, b = 1 and c = 1, then the x-intercept -c/a = 1 is greater than 0.
Since we don't have a unique solution, condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
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