GMAT Math : GMAT Quantitative Reasoning
Study concepts, example questions & explanations for GMAT Math
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Example Questions
Example Question #641 : Geometry
Find the slope of the line tangent to circle 
I) Circle
II) The area of circle f is 
Either statement alone 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 together 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.
Neither statement is sufficient to answer the question. More information is needed.
In this case, I and II give us a ton of information about the size of the circle, but we have no clue as to its location.
In order to know the slope of the tangent line, we need to know location of the circle, so we cannot solve this problem.
Example Question #1 : Other Lines
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.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH 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 #3 : Dsq: Calculating Whether Point Is On A Line With An Equation
Find whether the point 
I) 
II) 
Statement I is sufficient to answer the question, but Statement II is not sufficient to answer the question.
Neither statement is sufficient to answer the question. More information is needed.
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.
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 
Example Question #1 : Dsq: Calculating The Equation Of A Line
Find the equation of linear function 
I)
II) 
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.
Both statements are needed to answer the question.
Either statement is 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.
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 #2 : Other Lines
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
Statement 2 alone is sufficient.
Statement 1 alone is sufficient.
Together the two statements are sufficient.
Neither of the statements, together or separate, is sufficient.
Either of the statements 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 #651 : Geometry
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 #3 : Dsq: Calculating The Equation Of A Line
Find the equation for linear function 
I) 
II)
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.
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.
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:
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