GMAT Math : Perpendicular Lines
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Example Questions
Example Question #11 : Perpendicular Lines
Consider the lines of the equations
and
Are these two lines parallel, perpendicular, or neither?
Statement 1:
Statement 2:
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 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.
Since the two equations are in slope-intercept form, 
If 
If 
Example Question #12 : 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 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.
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 
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