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How long is MN?

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Bunuel
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How long is MN? [#permalink] New post   31 Jan 2016, 08:19
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E

Difficulty:

35% (medium)

Question Stats:

65% (01:12) correct 35% (01:29) wrong based on 96 sessions
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How long is MN?

(1) ON = 6 1⁄2
(2) MQ = 6

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Re: How long is MN? [#permalink] New post   31 Jan 2016, 12:00
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\(\triangle\) PQO and \(\triangle\) PMN are similar
Since \(\angle\)OQP =\(\angle\) NMP = 90
and \(\angle\) OPQ = \(\angle\) NPM (Common angle)
The corresponding sides of similar triangles are in proportion
(1) ON = 6 1⁄2
In right angled \(\triangle\) PQO ,
OP^2 = OQ^2 + QP^2
= 5^2 + 12^2
= 25 +144
= 169
OP= 13
NP = PO + ON
= 13 + 6.5 = 19.5
OQ/ MN = PO / PN
5/MN = 13 / 19.5 = 2/3
=>MN = 7.5
Sufficient
(2) MQ = 6
PQ/PM = OQ/ NM
12/18 = 5/NM = 2/3
MN = 7.5
Sufficient
Answer D
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Re: How long is MN? [#permalink] New post   06 Sep 2017, 23:40
Bunuel wrote:

How long is MN?

(1) ON = 6 1⁄2
(2) MQ = 6

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Attachment:
2016-01-31_1918.png


Two ways to approach similar triangles

St 1

Yes because OQ/MN = PO/PN

St 2

Another way

D
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Re: How long is MN? [#permalink]
06 Sep 2017, 23:40
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Bunuel
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