saintforlife wrote:
The value of x is to be randomly selected from the integers from 1 to 10, inclusive, and then substituted into the equation y = x^2 - 4x + 3. What is the probability that the value of y will be negative?
A. 1/10
B. 1/5
C. 1/4
D. 3/10
E. 3/5
We need to find that how many of the values of x from 1 to 10 make y negative.
y = x^2 - 4x + 3
We can split the positive and negative terms:
y = x^2 + 3 - 4x
For y to be negative, 4x needs to be greater than (x^2 + 3). We don't need to try x = 4 or greater since in those cases, x^2 + 3 will always be greater than 4x. Think of it this way
6*6 + 3 will be greater than 4*6; 7*7 + 3 will be greater than 4*7 etc
So we just need to figure out x = 1, 2 and 3
For x = 1 and 3, y = 0
For x = 2, y = -1
So only for one value of x, y will be negative.
Hence required probability = 1/10
Alternatively, you can think of the graph of a quadratic.
y = x^2 - 4x + 3 = (x - 3)(x - 1) will be a parabola facing upwards with roots at 1 and 3. So it will lie below the x axis only for x = 2.
_________________
Karishma
Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >