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How long is MN?

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How long is MN?  [#permalink]

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New post 31 Jan 2016, 08:19
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

62% (00:54) correct 38% (01:14) wrong based on 78 sessions

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Re: How long is MN?  [#permalink]

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New post 31 Jan 2016, 12:00
2
1
\(\triangle\) 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]

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New post 06 Sep 2017, 23:40
Bunuel wrote:
Image
How long is MN?

(1) ON = 6 1⁄2
(2) MQ = 6

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