GMAT Math : Lines
Study concepts, example questions & explanations for GMAT Math
All GMAT Math Resources
Example Questions
Example Question #41 : Lines
Consider linear functions 
I) 
II)
Is the point 
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.
Both statements are needed to answer the question.
Either statement is sufficient to answer the question.
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.
Consider linear functions h(t) and g(t).
I) 
II)
Is the point 
We can use II) and I) to find the slope of h(t)
Recall that perpendicular lines have opposite reciprocal slope. Thus, the slope of h(t) must be
Next, we know that h(t) must pass through (6,4), so lets us that to find the y-intercept:
Next, check if (10,4) is on h(t) by plugging it in.
So, the point is not on the line, and we needed both statements to know.
Example Question #1 : Dsq: Calculating Whether Point Is On A Line With An Equation
Line m is perpendicular to the line l which is defined by the equation 
(1) Line m passes through the point 
(2) Line l passes through the point 
Statements (1) and (2) TOGETHER are NOT sufficient.
EACH statement ALONE is sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Statement 1 allows you to define the equation of line m, but does not provide enough information to solve for 
if 
Example Question #1 : Dsq: Calculating The Equation Of A Line
Find the equation of linear function 
I)
II) 
Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.
Statement II is sufficient to answer the question, but Statement I is not sufficient to answer the question.
Either statement is 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.
Both statements are needed to answer the question.
To find the equation of a linear function, we need some combination of slope and a point.
Statement I gives us a clue to find the slope of the desired function. It must be the opposite reciprocal of the slope of 
Statement II gives us a point on our desired function, 
Using slope-intercept form, we get the following:
So our equation is as follows
Example Question #1 : Dsq: Calculating The Equation Of A Line
There are two lines in the xy-coordinate plane, a and b, both with positive slopes. Is the slope of a greater than the slope of b?
1)The square of the x-intercept of a is greater than the square of the x-intercept of b.
2) Lines a and b have an intersection at
Either of the statements is sufficient.
Statement 2 alone is sufficient.
Together the two statements are sufficient.
Statement 1 alone is sufficient.
Neither of the statements, together or separate, is sufficient.
Neither of the statements, together or separate, is sufficient.
Given that the square of a negative is still positive, it is possible for a to have an x-intercept that is negative, while still having a positive slope. The example above shows how the square of the x-intercept for line a could be greater, while having still giving line a a slope that is less than that of b.
Example Question #3 : Dsq: Calculating The Equation Of A Line
Line j passes through the point 
1) Line j is perpindicular to the line defined by
2) Line j has an x-intercept of
Statement 1 alone is sufficient.
Statement 2 alone is sufficient.
Together, the two statements are sufficient.
Neither of the statements, separate or together, is sufficient.
Either of the statements is sufficient.
Either of the statements is sufficient.
Either statement is sufficient.
Line j, as a line, has an equation of the form
Statement 1 gives the equation of a perpindicular line, so the slopes of the two lines are negative reciprocals of each other:
Statement 2 allows the slope to be found using rise over run:
Then, since the x-intercept is known:
Example Question #4 : Dsq: Calculating The Equation Of A Line
Find the equation for linear function 
I) 
II)
Statement II is sufficient to answer the question, but statement I is not sufficient to answer the question.
Either statement is 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.
Both statements are needed to answer the question.
Find the equation for linear function p(x)
I) 
II)
To begin:
I) Tells us that p(x) must have a slope of 16
II) Tells us a point on p(x). Plug it in and solve for b:
Example Question #5 : Dsq: Calculating The Equation Of A Line
Give the equation of a line.
Statement 1: The line interects the graph of the equation 
Statement 2: The line interects the graph of the equation 
STATEMENT 1 ALONE provides sufficient information to answer the question, but STATEMENT 2 ALONE does NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
BOTH STATEMENTS TOGETHER provide sufficient information to answer the question, but NEITHER STATEMENT ALONE provides sufficient information to answer the question.
STATEMENT 2 ALONE provides sufficient information to answer the question, but STATEMENT 1 ALONE does NOT provide sufficient information to answer the question.
EITHER STATEMENT ALONE provides sufficient information to answer the question.
BOTH STATEMENTS TOGETHER do NOT provide sufficient information to answer the question.
Assume both statements to be true. Then the line shares its 
making the 
The common 
The parabola therefore has two 
Example Question #1 : Dsq: Calculating The Slope Of A Line
Is the slope of the line 
Statement 1:
Statement 2:
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.
Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.
Therefore, the sign of 
The first statement means that 
The second statement - that 
Example Question #2 : Dsq: Calculating The Slope Of A Line
Does a given line with intercepts 
Statement 1:
Statement 2:
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.
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 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.
The slope of a line through 
From Statement 1 alone, we can tell that
so we know the sign of the slope.
From Statement 2 alone, we can tell that
But this can be positive or negative - for example:
but
Example Question #3 : Dsq: Calculating The Slope Of A Line
Does a given line with intercepts
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.
BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.
The slope of a line through
If 
Statement 1 is not enough to determine the sign of 
Case 1:
Case 2:
So if we only know Statement 1, we do not know whether 
If we know both statements, we can solve the system of equations as follows:
Therefore, we know 
All GMAT Math Resources
