[GMAT math practice question]
If a, b, and c are different positive integers, what is the value of a+b+c?
1) a^2+b^2+c^2=14
2) ab+bc+ca=11
=>
Condition 1)
We can assume a < b < c without loss of generality.
The maximum value of c is 3 and c^2 = 9
a^2 + b^2 = 5.
Then we have b = 2 and a = 1.
a + b + c = 1 + 2 + 3 = 6
Condition 2)
We can assume a < b < c without loss of generality.
ab + bc + ca = (a+b)c + ab = 11
Since a + b >= 3, the maximum value of c = 3.
If c = 3, ab + 3b + 3a = 11 or ab + 3a + 3b + 9 = 20.
We have (a+3)(b+3) = 20.
Then a = 1 and b = 2.
Thus a + b + c = 1 + 2 + 3 = 6.
Therefore the answer is D
Ans: D
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