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Is the perimeter of a triangle greater than 100?

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Is the perimeter of a triangle greater than 100?  [#permalink]

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New post 17 Jan 2016, 21:44
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A
B
C
D
E

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Question Stats:

48% (01:24) correct 52% (01:12) wrong based on 110 sessions

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Is the perimeter of a triangle greater than 100?


1) The shortest side is greater than 100/3
2) The longest side is greater than 50


* A solution will be posted in two days.

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Re: Is the perimeter of a triangle greater than 100?  [#permalink]

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New post 17 Jan 2016, 22:30
My Answer is D
Soln:
Sufficient:If the shortest side 100/3 then the other two sides are obviously greater than the shortest side, I.e 100/3. Thus sum of 100/3+ 2(100+/3) will be greater than 100.
Sufficient: If one of the side if 50 then the sum of other sides should be greater than the other side, I.e if A=50 B+C>50. Thus A+B+C=50+(50+)=100+
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Re: Is the perimeter of a triangle greater than 100?  [#permalink]

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New post 17 Jan 2016, 23:16
MathRevolution wrote:
Is the perimeter of a triangle greater than 100?


1) The shortest side is greater than 100/3
2) The longest side is greater than 50


* A solution will be posted in two days.


IMO (D)

Stat 1: It could be any triangle. Worst case Equilateral triangle with sides 33.4 each (coz > 33.3) which sums up to more than 100
Any other triangle would be more than 100

Stat 2: longest side is greater than 50 and if we consider the second side as say 49 then 50.1 (coz > 50) - 49 means the third side should be more than 1.1 . Add 50.1 + 49 + 1.2 and the result is more than 100.
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Re: Is the perimeter of a triangle greater than 100?  [#permalink]

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New post 19 Jan 2016, 18:52
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Is the perimeter of a triangle greater than 100?
1)The shortest side is greater than 100/3
2)The longest side is greater than 50

When it comes to a triangle, the sum of two sides is always longer than the other side. That is, if a, b, and c represent three sides of a triangle, it is a+b>c.

In the original condition, there are 3 variables(you need to figure out three sides since it’s a triangle), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2),
For 1), if a<b<c, c>b>a>100/3 -> a>100/3, b>100/3, c>100/3 -> a+b+c>100, which is yes and sufficient.
For 2), if a<b<c, a+b>c>50 -> a+b>50 and c>50. So, it makes a+b+c>100, which is also yes and sufficient. Since 1) =2), the answer is D.
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Re: Is the perimeter of a triangle greater than 100?  [#permalink]

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New post 13 Aug 2019, 16:26
MathRevolution wrote:
Is the perimeter of a triangle greater than 100?


1) The shortest side is greater than 100/3
2) The longest side is greater than 50


* A solution will be posted in two days.


My Approach :
A. Shortest side is 100/3. Let's say 34. Now this is the shortest so the next possible values can be 34,35. Sum is greater than 100. But wait the Question doesn't say the values are integer. Let's try 33.34*3 (or you can imagine 101/3) the sum is still greater than 100. Sufficient.

B. Longest side is greater than 50. Let's say 51. Now The other 2 sides can't be like 1,1 or 2,2 because sum of any 2 sides should be greater than the third side. So at the minimum we will be 27,25 as other 2 sides. The sum is still greater than 100. Sufficient.

Hence D
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Re: Is the perimeter of a triangle greater than 100?   [#permalink] 13 Aug 2019, 16:26
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