gmattesttaker2 wrote:
If the graph of y = x^2 + ax + b passes through the points (m, 0) and (n, 0), where m < n, what is the value of n - m ?
(1) 4b = a^2 - 4
(2) b = 0
What is the value of n-m?
(m,0) and (n,0) are the two points at which y=0 and the graph intersects the x-axis.
Thus, m and n are the x-intercepts of the graph.
Since m<n, n-m > 0.
Question rephrased:
What is the positive difference between the x-intercepts?
Statement 1: 4b = a²-4
Test easy cases.
Case 1: a=0
If a=0, we get:
4b = 0²-4
b=-1.
Substituting a=0 and b=-1 into y = x² + ax + b, we get:
y = x² + 0x - 1.
y = x² - 1.
Here, y=0 when x=-1 or x=1.
Thus, the x-intercepts are -1 and 1.
Result:
Positive difference between the x-intercepts = 1 - (-1) = 2.
Case 2: a=2
If a=2, we get:
4b = 2²-4
b=0.
Substituting a=2 and b=0 into y = x² + ax + b, we get:
y = x² + 2x + 0
y = x(x+2).
Here, y=0 when x=0 or x=-2.
Thus, the x-intercepts are -2 and 0.
Result:
Positive difference between the x-intercepts = 0 - (-2) = 2.
The cases above illustrate that -- given the constraint in statement 1 -- the positive difference between the x-intercepts must be 2.
SUFFICIENT.
Statement 2: b=0
In Case 2, b=0 and a=2.
In this case, the positive difference between the x-intercepts is 2.
Case 3: b=0 and a=1
Substituting a=1 and b=0 into y = x² + ax + b, we get:
y = x² + 1x + 0
y = x(x+1).
Here, y=0 when x=0 or x=-1.
Thus, the x-intercepts are -1 and 0.
Result:
Positive difference between the x-intercepts = 0 - (-1) = 1.
Since the positive difference is not the same value in each case, INSUFFICIENT.
The correct answer is
A.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at
[email protected].
Student Review #1
Student Review #2
Student Review #3
