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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

Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z
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23 Oct 2017, 04:50

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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. Please give me kudos. I need them to unlock gmatclubtests

Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z
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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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PARALLEL LINES.png [ 7.34 KiB | Viewed 507 times ]

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.

gmatclubot

Re: Is the line PQ parallel to the line SR? (1) w = q (2) y = z &nbs
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23 Oct 2017, 13:13