Data Sufficiency

Hi All,

We're told that in the xy-plane, Line K has a NEGATIVE SLOPE and passes through the point (-5, R). We're asked if the X-intercept of line K is positive. This is a YES/NO question. The answer to this question depends on the Slope of Line K and the value of R, meaning that we can TEST VALUES to answer it.

1) The slope of line K is -5.

While a slope of -5 is somewhat 'steep', we still don't know the value of R, so Line K may or may not have a positive X-intercept.
IF....
R = 1, then Line K will have a NEGATIVE X-intercept and the answer to the question is NO.
R = 1000, then Line K will have a POSITIVE X-intercept and the answer to the question is YES.
Fact 1 is INSUFFICIENT

2) R > 0

Fact 2 tells us nothing about the SLOPE of Line K, but both TESTs from Fact 1 can be used in Fact 2 IF the slope of Line K = -5:
IF....
Slope = -5 and....
R = 1, then Line K will have a NEGATIVE X-intercept and the answer to the question is NO.
R = 1000, then Line K will have a POSITIVE X-intercept and the answer to the question is YES.
Fact 2 is INSUFFICIENT

Combined, we already have 2 TESTs that 'fit' both Facts and gives us different answers (one "NO" and one "YES"), so no additional work is needed.
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

beater wrote: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 = (y2 - y1)/(x2 - x1), 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.

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.

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