Line L passes through the points A and B having coordinates (p,q) and

Question

Line L passes through the points A and B having coordinates (p,q) and (r,s), respectively. Is the slope of Line L positive ?

(1) p < 0 and q < 0
(2) r > 0 and s < 0

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RaghavKhanna · Answer

A(p,q) and B(r,s)

Slope of line passing through these points = \(\frac{s - q}{r - p}\)

If the slope of the line is positive, then:
Case 1: s - q > 0 and r - p > 0
Case 2: s - q < 0 and r - p < 0

Statement 1:
p < 0 and q < 0
Still no information about the sign of r and s

=> Statement 1 is insufficient

Statement 2:
r > 0 and s < 0
Still no information about the sign of p and q

=> Statement 2 is insufficient

Statement 1 & Statement 2:
p < 0 and q < 0
r > 0 and s < 0

=> r - p > 0
and,
s - q > 0 OR s - q < 0 (we do not know if s > q or s < q)

=> Statement 1 and Statement 2 together are insufficient

Answer: E

GMATinsight · Answer

Slope of Line passing through Points (p,q) and (r,s) = \frac{y_2 - y_2 }{ x_2 - x_1} = \frac{s - q }{ r - p} Question: Is \frac{s - q }{ r - p} > 0 ? Statement 1 : p < 0 and q < 0 No comparison of p, q with r, s hence NOT SUFFICIENT Statement 2 : r > 0 and s < 0 No comparison of p, q with r, s hence NOT SUFFICIENT COmbining the statements p < 0 and q < 0 and r > 0 and s < 0 i.e. Although r-p is positive BUT s-q may be positive or negative based on their absolute values hence NOT SUFFICIENT Answer: Option E

anthien128 · Answer

IMO E is the correct answer.

(1) This is just information of A. We do not know about B
 --> INSUFFICIENT

(2) This is just information of B. We do not know about A
 --> INSUFFICIENT

Combine (1) and (2) then we have r - p > 0 but we do not know about s - q (may be negative or positive). Therefore we cannot conclude anything about the slope.
 --> Combination of (1) and (2) is still INSUFFICIENT.

Loser94 · Answer

BOth statements are insufficient.

State1 :
P and q both are negative that means slope can be positive or negative
State 2 
r positive and s negative again slope can be positive and negative

using both state 
slope can be positive or negative depending on values of q and s.
since both are negative . if q>r then slope is negative
and if q<r then slope will be positive.

So Option E both are insufficient.

GMATWhizTeam · Answer

Solution Step 1: Analyse Question Stem • Line L passes through points A(p, q) and B (r, s). • We need to find if the slope of line L > 0 o Or, slope of the line L =\frac{q – s}{p-r} > 0 So we basically need to find whether signs of (q-s) and (p-r) are same or not. Step 2: Analyse Statements Independently (And eliminate options) – AD/BCE Statement 1: p < 0 and q < 0 • This statement gives no information about r and s. So, we cannot find if signs of (q-s) and (p-r) are same or not. Hence, statement 1 is NOT sufficient and we can eliminate answer Options A and D. Statement 2: r > 0 and s < 0 • This statement gives no information about p and q. So, we cannot find if signs of (q-s) and (p-r) are same or not. Hence, statement 2 is NOT sufficient and we can eliminate answer Options B. Step 3: Analyse Statements by combining. • From statement 1: p < 0 and q < 0 • From statement 2: r > 0 and s < 0 • On combining both statements, we get, o (p-r) < 0 o But we cannot decide the sign of (q-s), it can be negative or positive.  For example: If q = -3 and s = -2 then (q-s) = -3+2 = -1,which is negative.  However, if q = -2 and s = -3 then (q-s) = -2+3 = 1,which is positive. Thus, the correct answer is Option E.

KaramveerBakshi · Answer

Slope of line passing through points A (p,q) and B (r,s) = (r-p)/(s-q)

Statement (1) doesn't tell us anything about r and s. 
 Insufficient. 
Statement (2) doesn't tell us anything about p and q. 
 Insufficient.

Combining both statements, we get

(r-p)/(s-q) = {+ve - (-ve)}/{-ve - (-ve)}

The numerator will always be positive but the denominator can be positive, negative or even 0 depending on the values of s and q.

Insufficient.

Hence, the answer is Option (E).

kush09 · Answer

Line L passes through the points A and B having coordinates (p,q) and (r,s), respectively. Is the slope of Line L positive ?

Solution:
(1) p < 0 and q < 0
 -- Considering Statement 1 alone:
Based on only one point, we cannot find slope of line. It can be +ve or -ve. 
 Statement 1 alone is not sufficient.

(2) r > 0 and s < 0
 -- Considering Statement 2 alone:
Based on only one point, we cannot find slope of line. It can be +ve or -ve. 
 Statement 2 alone is not sufficient.

On Combining both the statement: 
 Line can have either +ve or -ve slope as we don't know relation between p&r and q&s.
 -- Combining is also not helpful.   
  
IMO answer is E.

dave13 · Answer

GMATWhizTeam  how is it possible that (p-r) < 0 is negative ?

GMATWhizTeam · Answer

Hey dave13

From statement 1 we know that p is negative, and from statement 2, we know that r is positive. 
So let's say p = -3 and r = 2, then p - r = negative number - positive number = -3 - 2 = -5 which is negative. That is why, (p-r) < 0.
I hope this helps.

Regards,
GMATWhiz Team

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Line L passes through the points A and B having coordinates (p,q) and

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GMAT Data Sufficiency (DS) Questions

Line L passes through the points A and B having coordinates (p,q) and

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