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31 Jan 2016, 08:19
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
65% (01:12) correct
35%
(01:29)
wrong
based on 96
sessions
History
Date
Time
Result
Not Attempted Yet
How long is MN?
(1) ON = 6 1⁄2
(2) MQ = 6
Attachment:
2016-01-31_1918.png [ 4.53 KiB | Viewed 1979 times ]
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
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
06 Sep 2017, 23:40
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Bunuel
Two ways to approach similar triangles
St 1
Yes because OQ/MN = PO/PN
St 2
Another way
D
