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# Which of the following must be true? I. Any of two lines which are p

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Math Expert
Joined: 02 Sep 2009
Posts: 52161
Which of the following must be true? I. Any of two lines which are p  [#permalink]

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13 Feb 2018, 05:08
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Difficulty:

45% (medium)

Question Stats:

43% (00:46) correct 57% (00:51) wrong based on 97 sessions

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Which of the following must be true?

I. Any of two lines which are parallel to a third line are also parallel to each other.
II. Any two planes which are parallel to a third plane are parallel to each other.
III. Any two lines which are parallel to the same plane are parallel to each other.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

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Posts: 867
Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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13 Feb 2018, 05:21
3
Bunuel wrote:
Which of the following must be true?

I. Any of two lines which are parallel to a third line are also parallel to each other.
II. Any two planes which are parallel to a third plane are parallel to each other.
III. Any two lines which are parallel to the same plane are parallel to each other.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

As there is a simple logic that governs parallel lines, we'll use it.
This is a Logical approach

I.
This is a basic definition of parallel lines and is true.

II.
This is also true for the same reason as above.
If we're not sure, we can try holding two sheets of paper above/below each other and SEE that this is true.
This is similar to drawing parallel lines on a sheet of paper to see that they must also be parallel.

III.
This is not true because a plane has infinitely many different directions.
For example, if you 'lift' the x-axis and y-axis 'up' above the xy plane they would still be parallel to it. (Formally, increase their 'z' value)
However, they are not parallel to each other.

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Posts: 272
Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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21 Feb 2018, 12:41
2
DavidTutorexamPAL wrote:
Bunuel wrote:
Which of the following must be true?

I. Any of two lines which are parallel to a third line are also parallel to each other.
II. Any two planes which are parallel to a third plane are parallel to each other.
III. Any two lines which are parallel to the same plane are parallel to each other.

(A) I only
(B) II only
(C) I and II only
(D) II and III only
(E) I, II, and III

As there is a simple logic that governs parallel lines, we'll use it.
This is a Logical approach

I.
This is a basic definition of parallel lines and is true.

II.
This is also true for the same reason as above.
If we're not sure, we can try holding two sheets of paper above/below each other and SEE that this is true.
This is similar to drawing parallel lines on a sheet of paper to see that they must also be parallel.

III.
This is not true because a plane has infinitely many different directions.
For example, if you 'lift' the x-axis and y-axis 'up' above the xy plane they would still be parallel to it. (Formally, increase their 'z' value)
However, they are not parallel to each other.

good principles +1

could you please, however, post any diagram that explains all the cases

thanks
examPAL Representative
Joined: 07 Dec 2017
Posts: 867
Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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21 Feb 2018, 13:14
3
gmatcracker2018 wrote:
good principles +1

could you please, however, post any diagram that explains all the cases

thanks

Thanks!
Here you go:
The diagram on the left shows standard parallel lines.
The diagram on the right shows parallel planes with an example of two sets of lines:
- the lines on the left are parallel to each other and to the different planes
- same goes for the lines on the right
- the lines on the left and on the right are not parallel to each other.
Attachments

temp.png [ 40.3 KiB | Viewed 698 times ]

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Joined: 24 Mar 2015
Posts: 272
Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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22 Feb 2018, 03:34
DavidTutorexamPAL wrote:
gmatcracker2018 wrote:
good principles +1

could you please, however, post any diagram that explains all the cases

thanks

Thanks!
Here you go:
The diagram on the left shows standard parallel lines.
The diagram on the right shows parallel planes with an example of two sets of lines:
- the lines on the left are parallel to each other and to the different planes
- same goes for the lines on the right
- the lines on the left and on the right are not parallel to each other.

thanks a lot +1
Re: Which of the following must be true? I. Any of two lines which are p &nbs [#permalink] 22 Feb 2018, 03:34
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