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

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

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New post 13 Feb 2018, 06:08
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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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Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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New post 13 Feb 2018, 06:21
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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.

(C) is our answer.
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Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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New post 21 Feb 2018, 13:41
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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.

(C) is our answer.


good principles +1

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

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

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New post 21 Feb 2018, 14:14
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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
temp.png [ 40.3 KiB | Viewed 1138 times ]


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

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New post 22 Feb 2018, 04:34
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
:-)
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Re: Which of the following must be true? I. Any of two lines which are p  [#permalink]

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New post 15 Apr 2019, 07:09
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Re: Which of the following must be true? I. Any of two lines which are p   [#permalink] 15 Apr 2019, 07:09
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