DHILLONRAVI1983 wrote:OG 2017 Diagnostic Quant question. Can this be solved algebraically?
In the XY plane, if line k has negative slope and passes through the point (-5, r), is the x intercept of line k positive?
1. the slope of line k is -5
2. r>0
We need to determine whether the x-intercept of line k is positive, given that line k has a negative slope and passes through the point (-5, r).
We can let the slope of line k be m and the x-intercept of line k be a; that is, line k passes through the point (a, 0). Using the slope formula m = (y_2 - y_1)/(x_2 - x_1), we have:
m = (0 - r)/(a -(-5))= -r/(a + 5)
Statement One Alone:
The slope of line k is -5.
Using the information in statement one, we can say the following:
-r/(a + 5) = -5
a + 5 = r/5
a = r/5 - 5
Since we don't know the value of r, we cannot determine the value of a.
For example, if r = 5, a = -4, which is negative. However, if r = 50, a = 5, which is positive. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.
Statement Two Alone:
r > 0
Knowing r is positive does not give us enough information to determine whether a, the x-intercept of line k, is positive. Statement two alone is not sufficient to answer the question. We can eliminate answer choice B.
Statements One and Two Together:
Looking at our work from statement one, and keeping in mind that r > 0 from statement two, we see that a can be positive or negative.
For example, if r = 5 then a = -4, which is negative. However, if r = 50 then a = 5, which is positive. The two statements together are still not sufficient to answer the question.
Answer:
E
