If 3 different integers are randomly selected from the set {1, 2, 3, 4, 5, 6}, what is the probability that a triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers?
A) 0.25
B) 0.3
C) 0.35
D) 0.40
E) 0.45
Source: www.gmatprepnow.com
Difficulty level: 650-ish
Answer: C
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If 3 different integers are randomly selected from the set {
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Brent Hanneson - Creator of GMATPrepNow.com
Number of ways to select 3 integers from the set\(= 6C3=20\)
A triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers when the sum of any 2 selected numbers is greater than the third number.
1. Cases possible when the longest side of the triangle is 6
\((6,5,4), (6,5,3), (6,5,2), (6,4,3)\)
2. Cases possible when the longest side of the triangle is 5
\((5,4,3), (5,4,2)\)
3. Cases possible when the longest side of the triangle is 4
\((4,3,2)\)
Total number of cases possible\(= 4+2+1=7\)
Probability\(= 7/20=0.35\)
A triangle can be constructed so that its 3 sides have the lengths of the 3 selected numbers when the sum of any 2 selected numbers is greater than the third number.
1. Cases possible when the longest side of the triangle is 6
\((6,5,4), (6,5,3), (6,5,2), (6,4,3)\)
2. Cases possible when the longest side of the triangle is 5
\((5,4,3), (5,4,2)\)
3. Cases possible when the longest side of the triangle is 4
\((4,3,2)\)
Total number of cases possible\(= 4+2+1=7\)
Probability\(= 7/20=0.35\)
