If each of the two lines L1 and L2 is parallel to line L3, which of th

Question

If each of the two lines L1 and L2 is parallel to line L3, which of the following must be true?

(A) Lines L1 , L2, and L3 lie in the same plane. 
(B) Lines L1 , ,L2 and L3 lie in different planes. 
(C) Line L1 is parallel to line L2 . 
(D) Line L1 is the same line as line L2. 
(E) Line L1 is the same line as line L3 .

Aren't answers D and E contradicting with questions?

FacelessMan · Answer

If each of the two lines L1 and L2 is parallel to line L3, it means L1 || L2 || L3. And thats exactly in answer choice C.

pushpitkc · Answer

The rest of the statements may or may not be true.
But, if both line m || p and n || p, line m must be definitely parallel to n(Option C)

GMATinsight · Answer

(A) Lines m, n and p lie in the same plane -  INCORRECT 
Reasons: m and p could be in one plane and n and p could be in another plane hence not necessarily they all will be in same plane

(B) Lines m, n and p are in different planes -  INCORRECT 
Reasons: m, n and p could all be in one plane as well

(C) Line m is parallel to line n -  CORRECT 
Since m and p are parallel on one part and n and p are parallel on other plane then there must be a plane containing lines n and m as well hence they must be parallel not necessarily in the same plane containing line p as well

(D) Line m is the same line as line n -  INCORRECT

(E) Line m is the same line as line p -  INCORRECT

ANswer: Option C

JeffTargetTestPrep · Answer

We have a theorem that says:

If two lines each are parallel to a third line, then they are parallel to each other.

Since line m and line n are both parallel to line p,lines m and n must also be parallel to each other.

Answer: C

t4hwg · Answer

How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...

m1033512 · Answer

There is a theoram which says

if two lines are parallel to a third line , then

all three lines are parallel to one another

means 
L1 ||L3

and L2 || L3

then ,

L1 || L2 || L3

hope this helps

award kudos if helpful

Posted from my mobile device

t4hwg · Answer

That seems rather arbitrary though doesn’t it? 
For example:
L1 is (0,2) through (5,2)
L2 is Y=2
L3 is Y=0

In this case, both lines 1 and 2 are parallel to 3 but not to each other. Is there some special line nomenclature that I’m missing?

dcummins · Answer

if L1 and L2 aren't parallel to each other then they cannot be parallel to L3 as they'd intersect at some point.

summerbummer · Answer

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Why cannot m, n, p be on the same plane? In the question it states that m & n are both // to p. C is true but why can't A be true?

ThatDudeKnows · Answer

summerbummer Does the question ask us for answer choice that CAN be true or one that MUST be true?

All of the answer choices CAN be true...but only one (C) MUST be.

A_Nishith · Answer

Cant Lines m, n and p lie in the same plane ?

Bunuel · Answer

They could. However, this is not necessarily the case, so option A is not always true.

Natansha · Answer

Hi Bunuel,  L1 and L2 can be coincident lines as well, making them both parallel to L3 BUT not parallel to each other, why is C correct then?

If each of the two lines L1 and L2 is parallel to line L3, which of th

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If each of the two lines L1 and L2 is parallel to line L3, which of th

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