DanaJ wrote: You get that x + 1/5 (200 - x) = 100

I think you might have misinterpreted the question - it asks us to subtract one fifth the number of incorrect answers, so we should have a minus sign:

x - 1/5 (200 - x) > 100
(6x/5) - 40 > 100
(6x/5) > 140
x > 5*140/6
x > 116.66....

So x must be at least 117. This is a question where you could also backsolve if you were uncertain how to set up the algebra. Considering the answer choices, you'd almost certainly want to start with either 116 or 117, since they're so close together - that suggests that one of them should be the right answer, while the other is there to trap someone who rounds down instead of up.

Pab2706, where are these questions from? You've posted a few recently, and some are poorly written (the percent question, for example), and one clearly had a mathematical error, as Dana pointed out (the x^2 + y^2 = 1 question).

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And an aside which is completely irrelevant to the current GMAT: the scoring system described in this question is similar to that which was often used in US standardized paper tests (SATs, for example, or the old GMAT paper tests). Those tests usually included a 1/4 point penalty for incorrect answers (though no penalty for unanswered questions) so that random guessing gave test takers neither an advantage nor a disadvantage - with five answer choices per question, if you guess at five questions, on average you'll get four wrong and one right, and therefore 1 point for the right answer, and a 4*(1/4) = 1 point penalty for the four wrong answers, meaning that 5 random guesses would, on average, neither increase or decrease your score. Of course that's not at all how the computer-based GMAT works, but you'll see that scoring system if you practice from an old GMAT paper test, and that's where the scoring system in the above question comes from.