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Yeah, there doesn't seem to be an easy way to just plug stuff in and solve algebraically. My method may shed some light though:
let the two numbers be x and y, and N be the answer
With the given information, I know that xy=N and that x+y = 11
which gives: x(11-x)=N 11x-x^2=N 0 = x^2 - 11x + N 0=(x ?)(x ?)
At this point, I had the following thoughts:
(A) -42 : to get -42, it must be (x + ?)(x - ?) so how can a positive and negative number add to -11 and yet still multiply together for -42? (B) -28 : similar thought process to (A) if you didn't start by evaluating A first (C) 12: (x + ?)(x + ?) or (x - ?)(x - ?) (D) 26 (E) 32
Truthfully, this is one of those questions where going through the entire calculation may not be necessary and just trying out numbers would be quicker.