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What is the length of RT in triangle RST with RS=12 and ST=4? (1) Perimeter of RST = 44 (2) RT is multiple of 7
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Follow posting guidelines (link in my signatures). Make sure to post the official answer (OA) everytime you post a new question.
As for the question, you are given that in triangle RST, RS=12, ST=4, RT=x=?
Per statement 1, perimeter = 44 . RT+RS+ST=44 ---> x+16=44 ---> x = 28. Sufficient. But this does not make sense. As per the property of triangles, 3rd side in a triangle must always lie between the positive difference of the other 2 sides and the sum of the other 2 sides --> |a-b|<c<a+b ---> 12-4 <x < 12+4 --> 8<x<16. Thus 28 can not be an allowed value.
Per statement 2, x=7p.
Using the concept mentioned in statement 1, |a-b|<c<a+b ---> 8< 7p < 16 , the only multiple of 7 between 8 and 16 is 14. Thus x=14. Sufficient.
D is thus the correct answer.
Another issue here: in GMAT DS, if both the statements are sufficient on their own, then both of them MUST give the same unique value. In this case, you are getting 2 different values for 2 individually sufficient statements. This is not allowed.
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