Geometry Guide pg 239 #19

[margaretmyoder]

19. In the xy-plane, Line n is a line that passes through the origin.

Which of the following statements individually provide(s) sufficient additional information to determine whether the slope of line n is greater than 1?

Indicate all such statements.

A) Line n does not pass through any point (a, b) where a and b are positive and a>b.
B) Line m is perpendicular to line n and has a slope of -1.
C) Line n passes through the point (c, d+1) where c and d are consecutive integers and c>d.

I chose C. However, the book says that B is also an answer to the question. However, if line m is perpendicular to n and has a slope of -1, then the slope of n has to be 1. If that is true, then the slope of the line is not greater than 1, it is equal to one. As a result, I did not choose B as an answer choice. Why is this a correct answer?

[tommywallach]

Hey Margaret,

So this is a logic question on top of a mathematics question (which is pretty common on the GRE).

They're asking what piece of information would be sufficient to ANSWER the question. Not to answer is YES, but to answer it AT ALL. Consider this:

What piece of information is sufficient to answer the question: "Is Sandra 40 years old?"

1) Sandra is older than 35
2) Sandra's age is even and between 39 and 41.
3) Sandra's age is 12.

Statement 2 is obviously sufficient to answer the question YES. But Statement 3 is ALSO sufficient, because it allows you to give a definitive NO answer.

In the case of the question, Statement 2 tells you that the slope of the line is definitively 1, which means it is definitively NOT greater than 1. We have answered the question using the statement.

-t