In the xy-plane line m passes through the points (2,2) and (r , s)

Question

In the xy-plane line m passes through the points (2,2) and (r , s) , where rs ≠ 0. Is r positive?

(1) The slope m is 1
(2) s is negative

CrackverbalGMAT · Answer

Constraints: rs ≠ 0. Therefore neither coordinates are 0.

Statement 1:   Slope (m) = 1

The slope of a line passing between any 2 points is given by  m = \frac{y_2 \space - \space y_1}{x_2 \space - \space x_1}

To get a slope of 1, r and s have to be both positive or both negative.

If r = 3 and s = 3, then slope =  \frac{3 \space - \space 2}{3 \space - \space 2} = 1 ; r is positive.

If r = -3 and s = -3, then slope =  \frac{-3 \space - \space 2}{-3 \space - \space 2} = \frac{-5}{-5} = 1 ; r is negative.

Therefore Statement 1 Alone is Insufficient  . Answer options could be B, C or E

Statement 2:   s is negative

Just by knowing that s is negative, we cannot know if r is positive or negative, as we do not know if the slope is positive or negative.

Therefore Statement 2 Alone is Insufficient  . Answer Options could be C or E.

Combining Both Statements:

Since we now know that the slope is positive and that s is negative, then we know that r also has to be negative. This answers our base question.

Therefore Both Statements together are Sufficient  .

Option C

Arun Kumar

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