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# If in the figure above OP = PQ, what is the length of PR?

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Math Expert
Joined: 02 Sep 2009
Posts: 53020
If in the figure above OP = PQ, what is the length of PR?  [#permalink]

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06 Sep 2018, 23:42
00:00

Difficulty:

45% (medium)

Question Stats:

68% (01:30) correct 32% (01:20) wrong based on 35 sessions

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If in the figure above OP = PQ, what is the length of PR?

(1) OR = RQ = 10

(2) Angle ROQ = 45

Attachment:

image005.jpg [ 4.93 KiB | Viewed 578 times ]

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Re: If in the figure above OP = PQ, what is the length of PR?  [#permalink]

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07 Sep 2018, 00:47
Bunuel wrote:

If in the figure above OP = PQ, what is the length of PR?

(1) OR = RQ = 10

(2) Angle ROQ = 45

Attachment:
image005.jpg

Question: what is the length of PR?

Given that P is midpoint of OQ

Statement 1: OR = RQ = 10

i.e. Triangle ORQ becomes an isosceles right angle triangle and hence the midpoint can be calculated as follows
Area of the triangle, (1/2)*OR*RQ = (1/2)*OQ*PR
i.e. (1/2)*10*10 = (1/2)*10√2*PR
i.e. PR = 5√2
SUFFICIENT

Statement 2: Angle ROQ = 45

i.e. triangle has angles 45º-45º-90º hence the reasoning used in statement 1 may be applied again to calculate the length of PR hence

SUFFICIENT

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Re: If in the figure above OP = PQ, what is the length of PR?  [#permalink]

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08 Sep 2018, 10:22
Bunuel wrote:

If in the figure above OP = PQ, what is the length of PR?

(1) OR = RQ = 10

(2) Angle ROQ = 45

Attachment:
image005.jpg

S1 - OR = RQ = 10
Consider triangles ORP and QRP
The triangles are congruent since angle O = Q; OR = RQ and OP = QP
Therefore angle OPR=QPR=90 deg.
We can find PR.
Sufficient.

S2 - Angle ROQ = 45
Angle RQP=ROQ=45 deg.
We cannot find PR since measure of any side is not given. Insufficient.
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Re: If in the figure above OP = PQ, what is the length of PR?  [#permalink]

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08 Sep 2018, 19:11
Similar problem I faced earlier and I made the same mistake. I didn't consider right angle symbol while solving the question.
And in another problem only box was mentioned and answer was provided taking shape of box rectangular.
So seeing such problems frequently, I have one question.
Should I always consider symbols and shapes as they are given in question in which nothing specifically mentioned?

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Re: If in the figure above OP = PQ, what is the length of PR?  [#permalink]

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08 Sep 2018, 20:00
gvij2017 wrote:
Similar problem I faced earlier and I made the same mistake. I didn't consider right angle symbol while solving the question.
And in another problem only box was mentioned and answer was provided taking shape of box rectangular.
So seeing such problems frequently, I have one question.
Should I always consider symbols and shapes as they are given in question in which nothing specifically mentioned?

Hi gvij2017
I am no expert. However, I would suggest to follow the below link and guidelines provided in OG.
https://gmatclub.com/forum/gmat-trick-r ... 01412.html
OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
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If in the figure above OP = PQ, what is the length of PR?  [#permalink]

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08 Sep 2018, 20:56
Bunuel wrote:

If in the figure above OP = PQ, what is the length of PR?

(1) OR = RQ = 10

(2) Angle ROQ = 45

Attachment:
image005.jpg

Statement I:

As OR = RQ & OP = PQ then by Similar Angles triangle -
$$PR/OR = OQ/PQ$$
Hence, $$PR = OQ$$

OQ = $$10\sqrt{2}$$

Statement II:

Again following similar triangle property as in Statement I, $$PR = OQ$$
But here, we can't determine the value of OQ.
Hence, Insufficient.
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If in the figure above OP = PQ, what is the length of PR?   [#permalink] 08 Sep 2018, 20:56
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# If in the figure above OP = PQ, what is the length of PR?

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