A line passes through (1,p), is its slope greater than 0?

Question

(1) The line passes through (p,13)
(2) The line passes through (p,-1)

gmatophobia · Answer

Statement 1

(1) The line passes through (p,13)

Slope = \frac{ y_2 - y_1 }{ x_2 - x_1}  =  \frac{13 - p }{ p - 1}

For certain values of p, the slope is greater than 0. For p = 13, the slope = 0

The statement is not sufficient.

Statement 2

(2) The line passes through (p,-1)

Slope = \frac{ y_2 - y_1 }{ x_2 - x_1}  =  \frac{ -1-p }{ p - 1}

For certain values of p, the slope is greater than 0. For p = -1, the slope = 0

The statement is not sufficient.

Combined

The statements combined

\frac{ -1-p }{ p - 1}  =  \frac{13 - p }{ p - 1}

Solving we can get an unique value of p. Sufficient.

Option C

Bunuel · Answer

And what would that solution be? Is the slope greater than 0?

gmatophobia · Answer

(p-1)(-1-p) = (p-1)(13-p)

(p-1)  = 0

(p-1) * -14 = 0

p = 1

The slope is undefined.

In fact we can see this behavior using the statements as well. For the same value of p (i.e. x coordinate), the line has two different values of y coordinate. Hence the line is parallel to Y axis.

A line passes through (1,p), is its slope greater than 0?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

A line passes through (1,p), is its slope greater than 0?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards