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Senior Manager
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Is the perimeter of a triangle greater than 1? 1). Two of [#permalink]
 10 Jun 2006, 21:59
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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 it is
(1) is insufficient to decide whether Per > 1 or not
(2) One height >1/2 so we have at least two sides > 1/2
so the perimeter>1
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VP
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gmat_crack wrote: 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 the sum of other two sides at least > than 1/2, making P greater than 1.
Last edited by Professor on 11 Jun 2006, 12:05, edited 1 time in total.
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D. Either stmt is sufficient
Stmt1 Analysis:
If a,b,c are the three sides and h1 and h2 are the two heights (lets say h1 divides b into b' and b", and h2 divides c into c' and c".
h1 > 1/3, h2 > 1/3
(a+b') > h1
(a+b') > 1/3 ... (a)
(c+b") > h1
(c+b") > 1/3.... (b)
Adding (a) & (b)
(a+c+b'+b") > 2/3
(a+b+c) > 2/3 which is less than 1.
Same can be done for h2.
Stmt1 is sufficient.
Stmt2 Analysis:
Using the same method as above for one height h > 1/2,
We can arrive @ (a+b+c) > 1
Stmt2 is sufficient.
Therefore D.
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VP
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Professor wrote: gmat_crack wrote: 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. Note that we just have to answer if (a+b+c)>1 or not.
Stmt 1 says it is not, stmt2 says it is. So separately both answer the question.
So, I think it should be D.
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Professor wrote: gmat_crack wrote: 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. 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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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008
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VP
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haas_mba07 wrote: Professor wrote: gmat_crack wrote: 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 the sum of other two sides at least > than 1/2, making P greater than 1.Note that we just have to answer if (a+b+c)>1 or not. Stmt 1 says it is not, stmt2 says it is. So separately both answer the question. So, I think it should be D. A is not suff. it doesnot tell about the third side.
if s1=0.32, s2=0.32 and s3 = 0.6, Perimeter is >1.
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ps_dahiya wrote: Professor wrote: gmat_crack wrote: 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.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. let me update: I mean "a side with 1/2 length makes the sum of other two sides at least > than 1/2, making P greater than 1". right? 
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