The strategy you should use on absolute value questions is totally level-dependent. If you're just aiming for an average Quant score, testing values should be fine - on easier questions it often works, and it's often fast. But if you're aiming for a high Quant score, you'll be seeing harder questions on test day, and on hard absolute value questions, testing numbers will either take far too long, or will simply not get you the answer. There are two mathematical approaches that can be used. The 'distance approach', the approach Bunuel used above to solve this question in 5 seconds, is most often the best approach. The 'cases method', which is what most people learn in school, can always be used, but it's often very awkward, so is best avoided unless strictly necessary. But it is necessary on occasion - I've seen a small number of real GMAT questions where the cases method is the only way to get an answer, so test takers aiming for Q51 scores probably should know how to use it.
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