Lines l1 and l2 eventually meet when extended to the right.

Question

lines.JPG Lines l1 and l2 eventually meet when extended to the right. Which of the following could be true? I. e = a II. a = f III. e + c = 180 (A) None (B) I only (C) II only (D) II and III only (E) I, II, and III

Bunuel · Accepted Answer

Look at the diagram below: Lines.png I. e = a --> as you can see this scenario is possible; II. a = f --> would be so if the lines l1 and l2 were parallel, since in this case a=c=f would be true; III. e + c = 180 --> would be so if the lines l1 and l2 were parallel, since in this case c=f and e+f=180 (also notice that since e=g then the sum of two interior angles of the triangle g and c can not be 180 degrees); Answer: B.

m760 · Answer

Straight ans is D.

SInce the lines are not parellel 
I can be eliminated

m760 · Answer

Good question and nice explanation
thanks

vinnik · Answer

Hi Bunuel ,

I am just trying to understand this question. 
If e = a, then by looking at the diagram can we say b=f, and c=g ?

Regards
Vinni

Bunuel · Answer

Yes, you are correct.

m3equals333 · Answer

Hi Bunuel, just out of curiosity, if the lines were organized similar to the attached, are statements 2 or 3 still not possible? As always, your help is most appreciated.

Bunuel · Answer

Essentially your drawing is the same as mine: if you lower the point of intersection you get the same image as in my post. Hence the logic discarding II and III would be the same too.

m3equals333 · Answer

ok, upon further inspection I see exactly what you're saying and why statement 2/3 are not possible, thanks!

WoundedTiger · Answer

Hi Bunuel,

If the question would have said which of the following must be true then Answer would have been be A.
Since the Question ask could be true clearly II and III statements can be ruled out cause we need the lines l1 and l2 to be parallel.

Is it correct??

Bunuel · Answer

Absolutely. If the question were which of the following MUST be true, then the answer would be A, none.

gmatprav · Answer

The point to note here is that l1 & l2 are NOT parallel. hence II & III cannot be true. I (a=e) could be true hence answer is B.

coldboy · Answer

Can anyone explain why a = e is correct?

rishit924 · Answer

Dear Sir,

I went with A because it is not given that l1 || l2.
Still, didn't get it why a=e in the above diagram?

Thanks in advance.

Lines l1 and l2 eventually meet when extended to the right.

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Lines l1 and l2 eventually meet when extended to the right.

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