Bunuel wrote:
If the function f is defined for all x by f(x) = ax^2 + bx − 43, where a and b are constants, what is the value of f(3)?
(1) f(4) = 41
(2) 3a + b = 17
It is one of those trick questions in which if you are not careful, you could fall for the trap and never know it. The impressions that "two unknowns need two equations to solve" and "a quadratic gives two solutions" are often exploited by the test makers. So be very wary about them.
Statement 1 is straight forward here:
f(x) = ax^2 + bx - 43
f(4) = 41 = 16a + 4b - 43
4a + b = 21
a and b could take different values so you cannot find f(3)
Statement 2 gives 3a + b = 17
You need to find f(3) = 9a + 3b - 43
Note that 9a + 3b = 3(3a + b) so you actually have the value of the desired expression.
So though statement 2 gives you an equation, you have enough information to solve for f(3).
It is good to write down what you need in such questions.
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Karishma
Veritas Prep GMAT Instructor
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