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PS question

by tvtt2010 » Wed Aug 17, 2011 8:21 pm
If two sides of a triangle have lengths 2 and 5, which of the following could be the perimeter of the triangle?
I. 9
II. 15
III. 19
A. None
B. I only
C. II only
D. II and III only
E. I, II, and III

I think the answer is B, because the triangle with 2 sides of 2 and 5 can have the third side of 2, then the perimeter can be 9. (in a triangle sum of two sides is more than the remain side, in this case the remain side should be smaller than 7)

Please check my answer.

Thanks
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by gmatboost » Wed Aug 17, 2011 8:35 pm
If the two known sides are 2 and 5, the third side must be

1. big enough: 2 + x > 5
2. not too big: 2 + 5 > x

In other words, it must be bigger than the difference of the known sides, but less than the sum

In this case, that means
[spoiler]1. x > 3
2. x < 7
So: 3 < x < 7[/spoiler]

The perimeter, which is x + 2 + 5 = x + 7
[spoiler]Add 7 to 3 < x < 7
10 < x < 14[/spoiler]
Answer: None
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by alaynaik » Wed Aug 17, 2011 8:51 pm
The other solution could be:

The sum of any two sides of a triangle is greater than the third side.

1) If the perimeter=9, then third side would be 2(i.e 2+5+x=9,hence,x=2)
So the three sides 2,2,5. Now, 2+2=4<5 and hence the condition of triangle is not satisfied.

2) Same is the case for options 15 & 19 where the third side would be 8 and 12 respectively. Both would not satisfy the condition for triangle.

Hence the OA would be A.None.
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by krishna8143 » Wed Aug 17, 2011 10:18 pm
yes alaynaik was absolutely ri8
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