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Bunuel
The three sides of a triangle measure x - 2, x + 1, and x + 2. Which of the following could x not equal?

A. 19
B. 17
C. 8
D. 4
E. 3

third side rule
x-2+x+1>x-2
2x-1>x+2
x>3
IMO E
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Bunuel
The three sides of a triangle measure x - 2, x + 1, and x + 2. Which of the following could x not equal?

A. 19
B. 17
C. 8
D. 4
E. 3

We recall that the sum of any two sides must be greater than the 3rd side. In other words, the sum of the two shortest sides must be greater than the longest side. We see that x - 2 and x + 1 are the two shortest sides, and x + 2 is the longest side; therefore, we have:

x - 2 + x + 1 > x + 2

2x - 1 > x + 2

x > 3

We see that 3 in choice E is the only number that is not greater than 3, so 3 can’t be the value of x.

Answer: E
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