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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
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Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p


(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
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
Expert Reply
Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p


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
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
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How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
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t4hwg wrote:
How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...



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
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
m1033512 wrote:
t4hwg wrote:
How can we assume L1 /= L2? If L1 and L2 are the same lines then they intersect infinitely and are therefore not parallel...



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


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?
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
if L1 and L2 aren't parallel to each other then they cannot be parallel to L3 as they'd intersect at some point.
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If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
GMATinsight wrote:
Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p


(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

---------------------------------------------------
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?
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
Expert Reply
summerbummer wrote:
GMATinsight wrote:
Bunuel wrote:
If each of the two lines m and n are parallel to line p, which of the following must be true?

(A) Lines m, n and p lie in the same plane
(B) Lines m, n and p are in different planes
(C) Line m is parallel to line n
(D) Line m is the same line as line n
(E) Line m is the same line as line p


(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

---------------------------------------------------
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?


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.
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
Cant Lines m, n and p lie in the same plane ?
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
Expert Reply
A_Nishith wrote:
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 .

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

­
They could. However, this is not necessarily the case, so option A is not always true.
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Re: If each of the two lines L1 and L2 is parallel to line L3, which of th [#permalink]
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