GMAT Math : Geometry
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Example Questions
Example Question #3 : Perpendicular Lines
Find the equation to a line perpendicular to line 
- The slope of line
is
.
- Line
goes through point
.
Both statements taken together are sufficient to answer the question, but neither statement alone is sufficient.
Each statement alone is sufficient to answer the question.
Statements 1 and 2 are not sufficient, and additional data is needed to answer the question.
Statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question.
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: Since the line we're looking for is perpendicular to line XY, our slope will be the inverse of line XY's slope 
The slope of our line is then 
Statement 2: We're provided with a point which will allow us the write the equation.
Example Question #11 : Perpendicular Lines
Consider the lines of the equations
and
Are these two lines parallel, perpendicular, or neither?
Statement 1:
Statement 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.
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.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 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.
Since the two equations are in slope-intercept form, 
If 
If 
Example Question #12 : Perpendicular Lines
You are given two lines. Are they perpendicular?
Statement 1: The product of their slopes is 1.
Statement 2: The sum of their slopes is 
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.
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.
The product of the slopes of two perpendicular lines is 
Statement 2 is neither necessary nor helpful, since the sum of the slopes is irrelevant to the question.
Example Question #13 : Perpendicular Lines
Are Line 1 and Line 2 on the coordinate plane perpendicular?
Statement 1: Line 1 is the line of the equation 
Statement 2: Line 2 has no 
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.
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 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.
We need to know the slopes of both lines to answer this question. Each statement gives information about only one line, so neither alone gives a definite answer.
Statement 1 tells us that Line 1 is vertical, since it is a line of the equation 
Example Question #104 : Coordinate Geometry
Are linear equations 
I) 
II) 
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
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.
Either statement is sufficient to answer the question.
Both statements are needed to answer the question.
To find whether these two functions are perpendicular we need to find each of their slopes.
Perpendicular lines have opposite, reciprocal slopes.
Use I) to find the slope of
Use II) to find the slope of
These are not opposite reciprocals, so 
Example Question #1 : Parallel Lines
Data Sufficiency Question
What is the slope of a line that passes through the point (2,3)?
1. It passes through the origin
2. It does not intersect with the line
statements 1 and 2 together are not sufficient, and additional data is needed to answer the question
each statement alone is sufficient
statement 2 alone is sufficient, but statement 1 alone is not sufficient to answer the question
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
each statement alone is sufficient
In order to calculate the equation of a line that passes through a point, we need one of two pieces of information. If we know another point, we can calculate the slope and solve for the 
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 #621 : Geometry
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.
EITHER statement ALONE is 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.
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.
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.
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