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18 Aug 2013, 12:05
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
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Question Stats:
45% (01:37) correct
55%
(01:41)
wrong
based on 288
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If AB=3, what is the shortest side of triangle ABC?
(1) AC=5
(2) The perimeter of ΔABC is 13.
(1) AC=5
(2) The perimeter of ΔABC is 13.
18 Aug 2013, 12:21
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blueseas
If AB=3, what is the shortest side of triangle ABC?
(1) AC=5
(2) The perimeter of ΔABC is 13.
(1) AC=5
(2) The perimeter of ΔABC is 13.
From F.S 1, we get a valid triangle for AC=5 and BC=4, and the smallest side is AB.
Again, for BC=2.1, we get another valid triangle and this time, the smallest side is BC. As we get 2 different answers, Insufficient.
From F.S 2, we know that AC+BC = 13-3 = 10. Now, we know that the difference of 2 sides must be less than the third side of a valid triangle.
Thus, as have |AC-BC|<3. Replacing the value of AC, we get \(|10-BC-BC|<3 \to -3<10-2BC<3 \to 3.5<BC<6.5\). Similarly, we will get the same range for AC. Thus, as both of them are greater than 3.5, the least value WILL BE for the side AB=3. Sufficient.
B.
General Discussion
jlgdr
Joined: 06 Sep 2013
Last visit: 24 Jul 2015
Posts: 1,316
Own Kudos:
Given Kudos: 355
Concentration: Finance
Schools: Wharton '17 (A) HBS '17 (WA$)
22 Apr 2014, 05:32
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mau5
blueseas
If AB=3, what is the shortest side of triangle ABC?
(1) AC=5
(2) The perimeter of ΔABC is 13.
(1) AC=5
(2) The perimeter of ΔABC is 13.
From F.S 1, we get a valid triangle for AC=5 and BC=4, and the smallest side is AB.
Again, for BC=2.1, we get another valid triangle and this time, the smallest side is BC. As we get 2 different answers, Insufficient.
From F.S 2, we know that AC+BC = 13-3 = 10. Now, we know that the difference of 2 sides must be less than the third side of a valid triangle.
Thus, as have |AC-BC|<3. Replacing the value of AC, we get \(|10-BC-BC|<3 \to -3<10-2BC<3 \to 3.5<BC<6.5\). Similarly, we will get the same range for AC. Thus, as both of them are greater than 3.5, the least value WILL BE for the side AB=3. Sufficient.
B.
Dear mau5, could you please elaborate on why |AC-BC|<3?
Thanks!
Cheers
J
You are absolutely correct. Thanks!! 
