Is the slope of Line K positive

[BTGmoderatorDC]

Is the slope of Line K positive ?

1) The product of the intercepts made by Line K is >= 0
2) The product of the intercepts made by Line K is <= 0

How will i identify the sufficient statement?

OA E

[elias.latour.apex]

In problems such as this one, it is best to start by asking ourselves: What do I need?

If we can determine the slope, we will know whether it is positive, negative, 0, or undefined. To determine the slope, we will need any two points OR a formula defining the line.

Does statement 1 give us 2 points? No. It gives us a wide range of points. This datum is insufficient.
Does statement 2 give us 2 points? No. This datum is also insufficient.

What about together? Together we have one point. We know that the line must go through (0,0) but we would need another point to get the slope.

Accordingly (E) is the best answer.

[Jay@ManhattanReview]

Is the slope of Line K positive ?

1) The product of the intercepts made by Line K is >= 0
2) The product of the intercepts made by Line K is <= 0

How will i identify the sufficient statement?

OA E

We have to determine whether the slope of Line K positive.

Let's take each statement one by one.

1) The product of the intercepts made by Line K is ≥ 0.

Case 1: The product of the intercepts made by Line K is > 0 or positive.

=> Both the interests are either positive or negative.

(a) Draw a straight line such that both the intercepts are positive, you would find that the slope is negative.
(b) Draw a straight line such that both the intercepts are negative, you would find that the slope is negative.

Case 2: The product of the intercepts made by Line K is 0.

=> The line passes through the origin (0, 0).

Draw few lines passing through the origin (0, 0). This opens the possibility of a positive, negative, 0, or undefined slope. Insufficient.

2) The product of the intercepts made by Line K is ≤ 0.

Having discussed (1), we see that Case (2) is also applicable here, thus, insufficient.

Same would be true when we combine both the statements.

The correct answer: E

Hope this helps!

-Jay
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