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Is the line PQ parallel to the line SR? (1) w = q (2) y = z

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Joined: 02 Sep 2009
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Is the line PQ parallel to the line SR? (1) w = q (2) y = z  [#permalink]

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New post 22 Oct 2017, 06:41
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (01:20) correct 26% (01:30) wrong based on 40 sessions

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Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z  [#permalink]

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New post 23 Oct 2017, 04:45
Bunuel wrote:
Image
Is the line PQ parallel to the line SR?

(1) w = q
(2) y = z

Attachment:
2017-10-22_1739.png


Is line PQ parallel to line SR? That is, is x = z?

Statement 1:
w = q
From the triangle PQR, x + q + y = 180 => x = 180 - q - y
z + w + y = 180 => z = 180 - w - y = 180 - q - y
Therefore, z = x
Lines PQ and SR are parallel.
Statement 1 is sufficient.

Statement 2:
y = z
x = 180 - q - y = 180 - q - z
But, this statement is not sufficient to know whether x = z

Therefore, answer is A.
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Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z  [#permalink]

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New post 23 Oct 2017, 04:50
2
IMO Option A
Using first statement w=q alternate interior angles are equal. So lines are parallel.
Second statement does not give us a condition for satisfying parallel lines So B not sufficient.
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Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z  [#permalink]

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New post 23 Oct 2017, 07:08
Think of lines QR and PR as transversals through lines PQ and SR. Two lines cut by a transversal will be parallel if all the acute angles are same and all the obtuse angles are same. Lines PQ and SR will be parallel if x=z and w=q.

Statement 1: as w=q so Lines PQ and SR are parallel. Sufficient
Statement 2: Insufficient to prove that x=z or w=q.

Answer: A
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Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z  [#permalink]

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New post 23 Oct 2017, 13:13
Bunuel wrote:
Image
Is the line PQ parallel to the line SR?

(1) w = q
(2) y = z

Attachment:
2017-10-22_1739.png


statement 1- w=q, then it will solve the question, using externally angle theorem, PQ is equal to SR.
statement 2- y=z, then it does not let us know about angle of line PQ and SR.

So the answer to the equation is A.
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Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z &nbs [#permalink] 23 Oct 2017, 13:13
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