GMAT Math : DSQ: Calculating whether point is on a line with an equation
Study concepts, example questions & explanations for GMAT Math
All GMAT Math Resources
Example Questions
Example Question #1 : Dsq: Calculating Whether Point Is On A Line With An Equation
Determine whether the points are collinear.
Statement 1: The three points are
Statement 2: Slope of line 
Statement 2 ALONE is sufficient, but statement 1 is 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 is not sufficient.
Statements 1 and 2 TOGETHER are NOT sufficient.
EACH statement ALONE is sufficient.
Points are collinear if they lie on the same line. Here A, B, and C are collinear if the line AB is the same as the line AC. In other words, the slopes of line AB and line AC must be the same. Statement 2 gives us the two slopes, so we know that Statement 2 is sufficient. Statement 1 also gives us all of the information we need, however, because we can easily find the slopes from the vertices. Therefore both statements alone are sufficient.
Example Question #2 : Other Lines
Given:
Find 
I) 
II) The 
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.
Both statements are needed to answer the question.
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.
Either statement is sufficient to answer the question.
By using I) we know that the given point is on the line of the equation.
So I) is sufficient.
II) gives us the y coordinate of the minimum. In a quadratic equation, this is what "c" represents.
Therefore, c=-80 and II) is also sufficient.
Example Question #1 : Other Lines
Find whether the point 
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.
Both statements are needed 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.
To find out if a point is on line with an equation, one can simply plug in the point; however, this is complicated here by the fact that we are missing the x-coordinate.
Statement I gives us our function.
Statement II gives us a clue to find the value of 
To see if the point 
This is not a true statement, so the point is not on the line.
Example Question #761 : Data Sufficiency Questions
Consider linear functions 
I) 
II)
Is the point 
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.
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.
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 #2 : 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 
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT 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.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is 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 
All GMAT Math Resources
