M23 #14 - Incorrect OA ?

Question

If line y=kx + b is parallel to line x=b + ky , which of the following must be true ?

A) k=b
B) k=1
C) b+k=0
D) |k|-1=0
E) k=-k

TheBirla · Answer

The OA is D.

OE : For lines to be parallel, their slopes must be equal. The second equation can be rewritten as y = x/k - b/k . Because slopes must be equal, k=1/k or k^2=1 or |k| = 1.

But for k=-1 the 2 equations are effectively the same (i.e. Not parallel)

Hence i think Ans should be B.

Mackieman · Answer

https://www3.wolframalpha.com/Calculate/MSP/MSP60719dh35a2104b6d3i00005fb1b4fe0d40cc56?MSPStoreType=image/gif&s=1&w=399&h=188

B is not true, |k| = 1 and k = 1 is not the same, rather |k| = 1 and {-k=1,k=1

TheBirla · Answer

Yes, when you solve the problem there will be 2 possible solutions to k, -1 and 1. But look at what is being asked in the q, are these lines parallel. And for k=-1, these lines are essentially the same y = -x + b. Hence not parallel.

Posted from my mobile device

Posted from my mobile device

Mackieman · Answer

Yeah you are right, sorry. Maybe someone can shed some light on this ?

ysr · Answer

D is the right answer

y=kx+b
y=x/k - b/k

Since slopes are equal k = 1/k
k^2=1
k=+1 or -1
Therefore |k| = 1 ---> |k|-1 = 0

If k=1 , we knw hw the equs would look like

y=x+b
y=x-b

If k=-1 , then two equations would look like

y = -x + b
y = -x +b

In both the scenarios the co-efficient of x is same , so the lines are parallel , the constant b can be +ve or -ve ....that does not matter . if a line is parallel , it does not mean that the constants must have the same sign . It depends on in which quadrant the lines are . A line passing through 1st and 4th quadrant can be parallel to line passing through 2nd and 3rd quadrant . In such scenarios , the slope of both the lines would be equal BUT NOT the constants......

ysr · Answer

Option B cannot be the answer as it has only +1 ....what about -1 ?

Mackieman · Answer

The question is whether a line can be both parallell and equal at the same time. It's obvious that if the lines are equal they have the same slope.

The common definition would be that two lines are parallell if they have the same slope and do not intersect.
Two equal lines would intersect at every point, so could you really say that two identical lines are parallell?

TheBirla · Answer

I agree that the sign of constant does not matter, but the constant itself does. And as Mackieman has pointed out already, if the constant of 2 parallel lines is the same, they are not parallel by definition, i.e. they are identical lines, BUT not parallel.

nishtil · Answer

I also have the same question. Can anyone put more light on it

boomtangboy · Answer

I also got B as the answer

But feel that D is right.

Anyone has the OA & Source ?

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

M23 #14 - Incorrect OA ?

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