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# If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR? (1) Q is th

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If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR? (1) Q is th  [#permalink]

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12 Sep 2018, 00:39
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35% (medium)

Question Stats:

81% (01:49) correct 19% (01:26) wrong based on 32 sessions

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If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR?

(1) Q is the midpoint of OS.
(2) QS = QO = 10

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Re: If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR? (1) Q is th  [#permalink]

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12 Sep 2018, 05:31

If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR?
Now in ∆PQO and ∆SQR..
∠OPQ = ∠QRS = 90
∠OQP= ∠RQS = opposite angles
Thus all angles are same and triangles are similar..
Similar triangles have all sides in SAME ratio..

(1) Q is the midpoint of OS.
So the sides are of same length
PQ = QR =6
Sufficient

(2) QS = QO = 10
Same as above
QR =6
Sufficient

D

Attachment:
image022.gif

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If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR? (1) Q is th  [#permalink]

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12 Sep 2018, 22:26
Bunuel wrote:

If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR?

(1) Q is the midpoint of OS.
(2) QS = QO = 10

Attachment:
image022.gif

Angle P=R=90
Angle OQP=RQS
Therefore all three angles of triangles OPQ and RQS are same.
Triangles are similar and Similar triangles have sides in the same ratio.
S1 - OQ=QS
Since triangles are similar and OQ=QS, PQ=QR=6
Sufficient.

S2 - QS = QO = 10, which is same info as S1 i.e. OQ=QS
QR=6.
Sufficient.
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If ∠OPQ = ∠QRS = 90 and PQ = 6, what is the length of QR? (1) Q is th   [#permalink] 12 Sep 2018, 22:26
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