If a, b, c are real numbers such that a < b <c and a + b + c = 6, ab + bc + ca = 9, then which among the following is definitely true?
a) 0 < a < 1
b) 1 < b < 3
c) 3 < c< 4
d) All of them
e) None of them
I am giving the solution, its a question of polynomial of degree 3 may be out of scope of GMAT. But I waana know what exactly the solution says and what may be the approach?
[spoiler]Let abc=t then a,b and c can be considered the roots of the eqn f(x) = x3 − 6x2 + 9x − t = 0
f(x) is decreasing in (1,3) . Also f(0) = f(3) = −t and f(1) > f(3) clearly now we can see option d) is right![/spoiler]
a) 0 < a < 1
b) 1 < b < 3
c) 3 < c< 4
d) All of them
e) None of them
I am giving the solution, its a question of polynomial of degree 3 may be out of scope of GMAT. But I waana know what exactly the solution says and what may be the approach?
[spoiler]Let abc=t then a,b and c can be considered the roots of the eqn f(x) = x3 − 6x2 + 9x − t = 0
f(x) is decreasing in (1,3) . Also f(0) = f(3) = −t and f(1) > f(3) clearly now we can see option d) is right![/spoiler]
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