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# Given four distinct lines, exactly two of which are parallel, which of

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Joined: 02 Sep 2009
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Given four distinct lines, exactly two of which are parallel, which of  [#permalink]

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01 Aug 2017, 13:33
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Difficulty:

75% (hard)

Question Stats:

27% (01:59) correct 73% (01:19) wrong based on 60 sessions

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Given four distinct lines, exactly two of which are parallel, which of the following could be the number of points where at least two of the lines intersect?

I. Three
II. Four
III. Five

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

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Re: Given four distinct lines, exactly two of which are parallel, which of  [#permalink]

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Updated on: 01 Aug 2017, 14:28
Ans E

Two lines are parallel.Rest two arenot.
The lines not parallel to each other can meet exactly atmost at One point.
Next,individually these two lines, can cross the paths of the two lines that lie parallel to each other,at two other points...giving Four such points of intersection.

Hence,in total,Five points.

Sent from my CP8676_I02 using GMAT Club Forum mobile app

Originally posted by Sangeeta2018 on 01 Aug 2017, 13:53.
Last edited by Sangeeta2018 on 01 Aug 2017, 14:28, edited 1 time in total.
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Joined: 11 Feb 2017
Posts: 188
Re: Given four distinct lines, exactly two of which are parallel, which of  [#permalink]

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01 Aug 2017, 14:18
Bunuel wrote:
Given four distinct lines, exactly two of which are parallel, which of the following could be the number of points where at least two of the lines intersect?

I. Three
II. Four
III. Five

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

if you extend the lines from backwards too , then u will find all the points of intersection
Senior SC Moderator
Joined: 22 May 2016
Posts: 2755
Given four distinct lines, exactly two of which are parallel, which of  [#permalink]

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Updated on: 07 Aug 2017, 06:02
Bunuel wrote:
Given four distinct lines, exactly two of which are parallel, which of the following could be the number of points where at least two of the lines intersect?

I. Three
II. Four
III. Five

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

Attachment:

linesintersect345.png [ 3.73 KiB | Viewed 981 times ]

Black means parallel.

EDIT: THIS POST IS INCORRECT. UPDATED BELOW.
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Originally posted by generis on 06 Aug 2017, 16:35.
Last edited by generis on 07 Aug 2017, 06:02, edited 1 time in total.
Senior SC Moderator
Joined: 22 May 2016
Posts: 2755
Given four distinct lines, exactly two of which are parallel, which of  [#permalink]

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07 Aug 2017, 05:56
genxer123 wrote:
Bunuel wrote:
Given four distinct lines, exactly two of which are parallel, which of the following could be the number of points where at least two of the lines intersect?

I. Three
II. Four
III. Five

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

Attachment:

linesintersect345.png [ 3.73 KiB | Viewed 930 times ]

Black means parallel.

Attachment:

linesintersect3and5.png [ 19.86 KiB | Viewed 926 times ]

UPDATE: THE ABOVE ANSWER, ALSO IN PRECEDING POST, IS NOT CORRECT. APPARENTLY I CAN'T COUNT MY OWN INTERSECTION POINTS. THE CORRECT ANSWER IS IN THIS POST. If you saw the original figure, you should still be able to see it in spoiler.

THE ANSWER IS D, I and III only.

1. If you have two parallel lines, they never intersect.

2. If you have two non-parallel lines, those two intersect each other eventually at exactly one point. +1 point of intersection

3. One of the non-parallel lines will intersect the two parallel lines in two places. +2 points of intersection

4. The other non-parallel line will also intersect the two parallel lines in two places. +2 points of intersection

TOTAL POSSIBLE is 1 + 2 + 2 = 5. That's Case 1 in NEW figure. (It doesn't matter which pair of non-parallel lines you move. I just chose two with labels A and D to make it easy to see.)

But you can use #2 and #3 so that the one point where the two non-parallel lines intersect is on one of the parallel lines

Where the one intersection point between the two non-parallel lines overlaps one of the parallel lines, you have decreased the number of intersection points to three. That's Case 2.

There is no way to make four intersection points with this set of lines. (You can get two points, obviously, by using two parallel and one non-parallel line.)

I dreamed about the original post's inaccuracy. I think I should be worried.

ANSWER D: I and III only
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Posts: 351
Re: Given four distinct lines, exactly two of which are parallel, which of  [#permalink]

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08 Aug 2017, 01:55
5 points - 2 parallel and 2 intersecting with point of intersection being above the parallel lines.
will wait for OA with OE
Re: Given four distinct lines, exactly two of which are parallel, which of   [#permalink] 08 Aug 2017, 01:55
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