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655-705 (Hard)|   Geometry|      
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gmat_crack
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Is the perimeter of a triangle greater than 1? Updated on: 11 Jul 2013, 11:30
Originally posted by gmat_crack on 10 Jun 2006, 21:59.
Last edited by Bunuel on 11 Jul 2013, 11:30, edited 2 times in total.
Edited the question and added the OA
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

75% (hard)

Question Stats:

47% (01:32) correct 53% (01:39) wrong based on 427 sessions

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Is the perimeter of a triangle greater than 1?

(1) Two of the heights are less than 1/3
(2) One of the heights is greater than 1/2
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B
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
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Professor
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Is the perimeter of a triangle greater than 1? Updated on: 11 Jun 2006, 12:05
Originally posted by Professor on 11 Jun 2006, 11:03.
Last edited by Professor on 11 Jun 2006, 12:05, edited 1 time in total.
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gmat_crack
Is the perimeter of a triangle greater than 1?

1). Two of the heights are less than 1/3
2). One of the heights is greater than 1/2
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B. a side with 1/2 length makes the sum of other two sides at least > than 1/2, making P greater than 1.
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Is the perimeter of a triangle greater than 1? 11 Jun 2006, 11:26
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Professor
gmat_crack
Is the perimeter of a triangle greater than 1?

1). Two of the heights are less than 1/3
2). One of the heights is greater than 1/2

B. a side with 1/2 length makes at least one of the other two sides more than 1/2, making P greater than 1.
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I agree that answer is B but if one side is greater than 1/2 then it does not mean that one more side will be greater than 1/2. Instead, sum of other two sides will be greater than 1/2 making perimeter greater than 1/2.
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Is the perimeter of a triangle greater than 1? 11 Jul 2013, 11:07
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can someone please explain the logic for this question
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Is the perimeter of a triangle greater than 1? 11 Jul 2013, 11:54
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veenu08
can someone please explain the logic for this question
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STATEMENT 1:
Two heights are less than 1/3
see in figure:==> 2 triangles are there ABC and DEF
Perpendiclar from B to AC..and perpendicular from C to AB===>LESS THAN 1/3...But we can take point much higher shown....lets perpendicular from A to BC..is 100 ..SO IN THIS case perimeter you can see will be more than 1.
take second triangle DEF ===>IN this all the heights are very smalll===>you can make very small triangle whose perimeter is less than 1.
hence statement 1 is not sufficient.


STATEMENT 2:
Triangle AMC and BMC are right angled triangle with AC and BC as hypotenuses respectively. Hence, both AC and BC are greater than CM. If the height CM is greater than 1/2 then the sides AC and BC must be greater than 1/2 too. Thus the perimeter of the triangle must be greater than 1. ==>Sufficient.
hence B

HOPE IT HELPS
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Is the perimeter of a triangle greater than 1? 11 Jul 2013, 12:10
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veenu08
can someone please explain the logic for this question
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Is the perimeter of a triangle greater than 1?

(1) Two of the heights are less than 1/3. Well, we can have a tiny triangle with the perimeter less than 1 but we also can have a right triangle with legs (heights) bit less than 1/3 = 0.(3). In this case hypotenuse wold be a bit less than 0.47 and the perimeter would be more than 1. Not sufficient.

(2) One of the heights is greater than 1/2. Consider the easiest case:



AB > 1/2, BC = hypotenuse > AB, thus the perimeter is for sure greater than 1. Sufficient.

Answer: B.

Hope it's clear.

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Is the perimeter of a triangle greater than 1? 23 Sep 2025, 19:46
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