Hey Ricky,
First off, I love that the two posters on this thread thus far are Rickey and Rockey. That could be a TV show in and of itself, if only for the purposes of alliteration.
Rockey's suggestion to focus on the fundamentals is a great one. The harder CR questions tend not to require a different thought process than the more moderate ones; they just make the process of doing so a bit more uncomfortable and difficult. The strategy should be the same, though:
1) Read the question stem first so that you know which type of question you're answering, and can focus on the important parts of the passage.
2) If you're asked to strengthen or weaken the conclusion, or explain the discrepancy, make sure you pay particular attention to the conclusion/discrepancy.
3) Eliminate answer choices that are out of scope of the conclusion, and select the answer that answers the question / fits the conclusion most directly.
Now, that's a whole lot easier said than done when questions become more difficult. Like Rockey mentioned, you'll want to pay attention to the mistakes you're making on these harder questions to see which devices that the questions use to trip you up. A few classics include:
1) Getting you to misread the conclusion or infer your own limits on it. Make sure that you precisely understand the conclusion in its entirety and don't infer anything that's not there. As humans, we're susceptible to wanting to prove universal truths - the biggest, tallest, fastest, first, last of anything. Make sure that if the conclusion simply says "single cell organisms existed in prehistoric Australia" that that is all you try to prove; you'll be tempted to try to prove that "the first organisms" existed there. Similarly, check your other biases - altruism, fairness, etc. - that may skew you toward a different conclusion. If the conclusion is that "we can only achieve true healthcare reform through universal coverage" you may read that as "we should mandate universal healthcare coverage". The conclusions aren't exactly the same - the first is that there is only one way to get it done; the second proposes that it ought to happen, but may not be the only way to achieve the result. That subtle difference could be the difference between two answer choices, and the authors of the test know that many will tend toward the second.
2) Answer choices for which the opening clause seems irrelevant, but the second half drives it home (after many have already eliminated it and stopped reading). Say that you need a statement that suggests that citrus fruits can have negative health consequences. A correct-but-difficult answer choice may begin: "A species of orangutan living in South Asia has been known to develop ulcers by the age of four, a condition that researchers attribute to the acidic nature of its citrus-heavy diet." As you're scanning the answers, that lead-in about orangutans seems woefully irrelevant, but the entire answer does support that citrus fruits can have negative health implications. The authors of that answer choice know that, by taking their sweet time to get to the point, they'll convince quite a few examinees to eliminate that answer without reading the whole thing.
3) Correct answers that leave something to be desired. Say that the premises of an argument lead you to the conclusion that "some members of Congress are guilty of treason". That's a newspaper headline, and something you'll be almost excited to be able to answer. The authors of the test may, then, try to sneak by you a more modest correct answer like "some citizens are traitors". It's definitely a logical conclusion, but not as epic as what you know you can prove, so you may be inclined to eliminate it in search of something more compelling, and take a flier on an answer choice that isn't quite 100%, but is surely more exciting, like "Congress is under the control of traitors" or "several senators are traitors". Beware of answer choices that bait you toward something more exciting at the expense of eliminating a more understated answer that is definitely true.
Look for these and other types of devices that are getting you down, and remember that focusing on the essentials is key. Each of these is a way to get you to stray from the overall Critical Reasoning methodology, so stay true to what you know works.
Brian Galvin
GMAT Instructor
Chief Academic Officer
Veritas Prep
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