GMAT Math : Lines
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Example Questions
Example Question #1 : Dsq: Calculating The Equation Of A Parallel Line
Find the equation of the line parallel to the following line:
I) The new line passes through the point 
II) The new line has a 
Neither statement is sufficient to answer the question. More information is needed.
Both statements are needed to answer the question.
Either statement is sufficient to answer the question.
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Statement I is sufficient to answer the question, but statement II is not sufficient to answer the question.
Either statement is sufficient to answer the question.
To find the equation of a parallel line, we need the slope and the y-intercept.
Parallel lines have the same slope, so we have that.
I and II each give us a point on the graph, so we could find the equation of the line through either of them.
Example Question #743 : Data Sufficiency Questions
Find the equation of the line 
- The slope of line
is
.
- Line
goes through point
.
Each statement alone is sufficient to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 1 alone is sufficient, but statement 2 alone is not sufficient to answer the question.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Statement 1: We're given the slope line AB, because we are ask for the equation of the line we need more than just the slope of the line. Therefore, this information alone is not sufficient to write an actual equation.
Statement 2: Using the information from statement 1 and the points provided in this statement, we can answer the question.
Example Question #4 : Dsq: Calculating The Equation Of A Parallel Line
Given 
I)
II) 
Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.
Both statements are needed to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
Either statement is sufficient to answer the question.
Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.
Both statements are needed to answer the question.
We are asked to find the equation of a line related to another line.
Statement I tells us the two lines are parallel. This means they have the same slope
Statement II gives us a point on our desired line. We can use this to find the line's y-intercept, which will then allow us to write its equation.
Plug all of the given info into slope-intercept form and solve for b, the line's y-intercept:
So our equation is:
Example Question #741 : Data Sufficiency Questions
You are given two lines. Are they parallel?
Statement 1: The product of their slopes is 
Statement 2: One has positive slope; one has negative slope.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Two parallel lines must have the same slope. Therefore, the product of the slopes will be the product of two real numbers of like sign, which must be positive. Each of the two statements contradicts this, so either statement alone answers the question.
Example Question #21 : Lines
One line includes the points 
1)
2)
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is not sufficient.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is not sufficient.
EITHER statement ALONE is sufficient to answer the question.
The lines are parallel, so their slopes are equal.
The slope of the first is 
The slope of the second is 
Set the two equal to each other:
If you know that 
Cross-multiply and solve:
If you know that 
Therefore, either statement alone is sufficient to answer the question.
Example Question #743 : Data Sufficiency Questions
You are given distinct lines 
Statement 1: Both lines have slope 3.
Statement 2: Line 
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Two lines can be determined to be parallel, perpendicular, or neither from their slopes.
Assume Statement 1 alone is true. Since these distinct lines have the same slope, they are parallel.
Assume Statement 2 alone is true. No information about the slopes of the lines can be determined from one single point, so Statement 2 alone is insufficient.
Example Question #747 : Data Sufficiency Questions
You are given distinct lines 
Statement 1: Line 
Statement 2: Both lines have 
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Two lines can be determined to be parallel, perpendicular, or neither from their slopes.
Assume Statement 1 alone. Parallel lines must have the same slope, so this choice can be eliminated. The slopes of perpendicular lines must have product 
Assume Statement 2 alone. Since the lines have at least one point in common, they are not parallel, but this is the only choice that can be eliminated.
Example Question #111 : Coordinate Geometry
You are given distinct lines 
Statement 1: Line 
Statement 2: Line 
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Two lines are parallel if and only if they have the same slope, and perpendicular if and only if their slopes have product 
Assume Statement 1 alone. Since the product of the slopes is 
Statement 2 alone is unhelpful, since no information about the slope of a line can be determined from only one point.
Example Question #749 : Data Sufficiency Questions
You are given two distinct lines, 
Statement 1: The absolute value of the slope of Line 
Statement 2: The absolute value of the slope of Line 
BOTH statements TOGETHER are insufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Assume both statements are true. Then three things are possible:
Case 1: Both lines will have slope 1, or
Case 2: Both lines will have slope
In either case, since the lines have the same slope, they are parallel.
Case 3: One line has slope 1 and one has slope
In this case the lines are perpendicular.
The two statements therefore provide insufficient information.
Example Question #7 : Dsq: Calculating Whether Lines Are Parallel
You are given distinct lines 
Statement 1: Line 
Statement 1: Line 
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
EITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
BOTH statements TOGETHER are insufficient to answer the question.
Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
The answer to the question depends on the slopes of the lines—parallel lines have the same slope, and perpendicular lines have slopes that have product 
From Statement 1 alone, we only know one point of each line, so no information about their slopes can be determined; the same holds for Statement 2.
Assume both statements are true. Then we know two points of each line—specifically, both intercepts—from which we can determine the slope of each by way of the slope formula. After doing so, we can use the slopes to answer the question.
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