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Thread: From the OCTOBER 2012 SAT

20130807, 10:23 #1
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From the OCTOBER 2012 SAT
[considered a level 5 (range 15, 5 being highest difficulty) by the College Board]
The lengths of two sides of a triangle are 5 and 12,
and the length of the third side is an integer. What
is the greatest possible perimeter of the triangle?
(A) 22
(B) 29
(C) 30
(D) 33
(E) 34

20130807, 23:31 #2
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I thought that this was one of the easier problems so I would have given it a level of 1. Since it is rated a 5, I am guessing that I am totally overlooking something....my life story

20130808, 08:31 #3
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You aren't overlooking anything...your answer is correct. The triangle is not necessarily a right triangle.
If it were, the lengths would have been 51213, making the perimeter 30. But, the length of the other side could be 16 as you pointed out. The math rule is that the sum of any two sides is larger than the third. That rules out 17 as you realized.
I suspect they classified this as difficult because many students immediately think it's 51213 because they a few triples in their mind and under test pressure would have jumped on that (wrong) answer.