April 15th, 2010 | 
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We’ve covered, in an earlier articles, how to deal with the simplest formal logic statement: If X, then Y. But what happens when our necessary or sufficient factors become more complicated? Let’s look at a couple of examples, using the idea of a vegetable salad. The simplest statement and its contrapositive might look like this:
If the salad has lettuce, then it has tomatoes.
If the salad has no tomatoes, then it has no lettuce.
Now let’s add more vegetables (and more complicated logic):
If the salad has lettuce or spinach, then it has tomatoes and peppers.
Here’s an important idea: when you are forming a contrapositive, you already know that the necessary and sufficient factors are switched around and negated. But now you also have to remember that “and” becomes “or,” and vice versa. So the statement above becomes:
If the salad has no tomatoes or no peppers, then it has no lettuce and no spinach.
I find it extremely helpful to individually negate each element of the statement; otherwise, it’s easy to get confused. For instance, if I only negate the first part of the statement above and say to you, “If the salad has no tomatoes or peppers…” you might interpret that as meaning that neither of those vegetables should be in the salad. But in formal logic terms, it would technically mean that I either want peppers or no tomatoes. Neither of those ideas, though, is what I mean to say in the contrapositive; the intended meaning is that I want no tomatoes or no peppers.
The pairing of “neither” and “nor” can also cause some consternation. The easiest way to deal with that is to remember that “neither X nor Y” is the same thing as “no X and no Y.” The example above can be rephrased as follows:
If the salad has no tomatoes or no peppers, then it has neither lettuce nor spinach.
So if you need to negate a “neither/nor” statement, the “nor” becomes “or” just as it would if the statement said “and.”
What if the sentence isn’t written in the order in which we expect to find the elements? For instance, how do we interpret a sentence that says:
The salad has cucumbers if it has onions.
Here we can take the word “if” and read the statement that follows it as the sufficient element. We can turn that sentence into this:
If the salad has onions, then it has cucumbers.
A final issue is the phrase “only if.” Let’s go back to our vegetable salad, and look at the following sentence:
The salad has carrots only if it has mushrooms.
Here, you can’t interpret “if” as signaling the sufficient element. “Only if” statements are interpreted differently than regular “if” statements. The “only if” statement above means the same thing as this:
If the salad has carrots, then it has mushrooms.
These ideas flesh out the basics of formal logic. To recap, here are the thoughts that you need to remember:
- When forming a contrapositive, turn “and” into “or” and vice versa.
- “Neither X nor Y” means “No X and no Y.”
- “X only if Y” means “If X then Y.”
Just remember that, as with everything on the GMAT, formal logic becomes much easier with Grockit GMAT practice, so keep working on it!
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The flipside of the “strengthen” question coin on the GMAT is the “weaken” question. The same set of evidence and conclusion can easily be used for either question type, so it’s always a good idea to start by reading the question itself first, to determine the task before you go to the argument. After that, your approach is almost identical to the way that you would approach a strengthen question. Take this question, for example:
Healica, a new drug that can cure a common disease that until now has been fatal for 50% of those infected, is made from the root of the New Zealand banananut tree. The banananut tree is rare in New Zealand, and large quantities of the root are necessary in order to make Healica. Therefore, if Healica remains in production, the banananut tree will eventually become extinct.
If true, which of the following most calls into question the conclusion above?
a) The company that holds the patent to Healica has exclusive rights to produce the drug for another 10 years.
b) Healica is expensive, and is not currently covered by most major insurance plans.
c) Banananut leaves are considered a gourmet delicacy in many parts of the world.
d) The banananut tree, although native to New Zealand, can easily be grown in other parts of the world.
e) Producing Healica is time-consuming and expensive for the drug manufacturer.
You should always read the question first, and here the commonly-used phrase “calls into question” means that this question is asking for a weakener.
Looking at the argument, we can see from the clue word “therefore” that the conclusion is the last sentence of the argument: “if Healica remains in production, the banananut tree will eventually become extinct.” Now our job is to find a way to attack the argument, and the easiest way to do that is to identify an existing weakness and exploit it.
Here, as in many arguments on the GMAT, the argument has an unstated assumption. The evidence states that the banananut tree is “rare in New Zealand,” and concludes that extinction will occur because of that. But for something to be extinct, it must not exist anywhere in the world, and we only have evidence about the tree’s growth in one country. The unstated assumptions are that the tree doesn’t grow anywhere else, and that growth can’t keep up with the demand for the trees. A great way to weaken the argument, then, is to attack one of those assumptions.
a) The company that holds the patent to Healica has exclusive rights to produce the drug for another 10 years.
This choice would require another assumption in order to weaken the conclusion: that the one company producing Healica would not produce enough of it to kill off the banananut tree. Weakeners, like strengtheners, shouldn’t require so much work to fit into the argument.
b) Healica is expensive, and is not currently covered by most major insurance plans.
This choice, like choice a), is not closely enough related to the argument.
c) Banananut leaves are considered a gourmet delicacy in many parts of the world.
This choice makes it more likely that the trees will be in demand and will face extinction. The argument is strengthened, not weakened, by this choice.
d) The banananut tree, although native to New Zealand, can easily be grown in other parts of the world.
This is the correct answer, since it exploits the unstated assumptions by explicitly disproving that one of them.
e) Producing Healica is time-consuming and expensive for the drug manufacturer.
This choice has the same problem as choices a) and b): it takes extra assumptions to fit it into the argument, and that’s not what we want.
If you find yourself taking several extra logical steps to explain how an answer choice relates back to the argument and makes the conclusion less likely to follow from the evidence, then the answer choice is probably not close enough to the text of the argument as written. Remember: stay close to the internal logic of the argument, and don’t bring in specialized outside knowledge! The test is written so that each question belongs in its own little world, and outside knowledge is rarely relevant to finding the correct answer.
A final word on weakeners: remember that the correct answer just has to make the conclusion less likely to follow from the evidence; it doesn’t need to completely disprove the conclusion, although sometimes it will. So make sure that you’re not looking for unnecessarily extreme answers.
Check out Grockit for more GMAT verbal practice. Check out Andrea’s Strengthening your Strengthen Muscles too!
The flipside of the “strengthen” question coin on the GMAT is the “weaken” question. The same set of evidence and conclusion can easily be used for either question type, so it’s always a good idea to start by reading the question itself first, to determine the task before you go to the argument. After that, your approach is almost identical to the way that you would approach a strengthen question. Take this question, for example:
Healica, a new drug that can cure a common disease that until now has been fatal for 50% of those infected, is made from the root of the New Zealand banananut tree. The banananut tree is rare in New Zealand, and large quantities of the root are necessary in order to make Healica. Therefore, if Healica remains in production, the banananut tree will eventually become extinct.
If true, which of the following most calls into question the conclusion above?
a) The company that holds the patent to Healica has exclusive rights to produce the drug for another 10 years.
b) Healica is expensive, and is not currently covered by most major insurance plans.
c) Banananut leaves are considered a gourmet delicacy in many parts of the world.
d) The banananut tree, although native to New Zealand, can easily be grown in other parts of the world.
e) Producing Healica is time-consuming and expensive for the drug manufacturer.
You should always read the question first, and here the commonly-used phrase “calls into question” means that this question is asking for a weakener.
Looking at the argument, we can see from the clue word “therefore” that the conclusion is the last sentence of the argument: “if Healica remains in production, the banananut tree will eventually become extinct.” Now our job is to find a way to attack the argument, and the easiest way to do that is to identify an existing weakness and exploit it.
Here, as in many arguments on the GMAT, the argument has an unstated assumption. The evidence states that the banananut tree is “rare in New Zealand,” and concludes that extinction will occur because of that. But for something to be extinct, it must not exist anywhere in the world, and we only have evidence about the tree’s growth in one country. The unstated assumptions are that the tree doesn’t grow anywhere else, and that growth can’t keep up with the demand for the trees. A great way to weaken the argument, then, is to attack one of those assumptions.
a) The company that holds the patent to Healica has exclusive rights to produce the drug for another 10 years.
This choice would require another assumption in order to weaken the conclusion: that the one company producing Healica would not produce enough of it to kill off the banananut tree. Weakeners, like strengtheners, shouldn’t require so much work to fit into the argument.
b) Healica is expensive, and is not currently covered by most major insurance plans.
This choice, like choice a), is not closely enough related to the argument.
c) Banananut leaves are considered a gourmet delicacy in many parts of the world.
This choice makes it more likely that the trees will be in demand and will face extinction. The argument is strengthened, not weakened, by this choice.
d) The banananut tree, although native to New Zealand, can easily be grown in other parts of the world.
This is the correct answer, since it exploits the unstated assumptions by explicitly disproving that one of them.
e) Producing Healica is time-consuming and expensive for the drug manufacturer.
This choice has the same problem as choices a) and b): it takes extra assumptions to fit it into the argument, and that’s not what we want.
If you find yourself taking several extra logical steps to explain how an answer choice relates back to the argument and makes the conclusion less likely to follow from the evidence, then the answer choice is probably not close enough to the text of the argument as written. Remember: stay close to the internal logic of the argument, and don’t bring in specialized outside knowledge! The test is written so that each question belongs in its own little world, and outside knowledge is rarely relevant to finding the correct answer.
A final word on weakeners: remember that the correct answer just has to make the conclusion less likely to follow from the evidence; it doesn’t need to completely disprove the conclusion, although sometimes it will. So make sure that you’re not looking for unnecessarily extreme answers.
Check out Grockit for more GMAT verbal practice. Check out Andrea’s Strengthening your Strengthen Muscles too!
In today’s competitive job market, even an MBA might not seem like enough to get you the kind of job that you want. If you’re looking for something to set you apart from the crowd, a JD/MBA might be an appealing option to you. But what is involved in earning those degrees jointly, and what can holding them do for your academic experience and your career trajectory?
If you’re interested in pursuing a joint degree, the first obvious step is to look for schools that offer the JD and MBA programs together. Not all business schools work together with law schools to create joint programs, so you’ll want to carefully evaluate the schools to which you’re planning to apply. Usually, there’s a specific liaison for the joint program working out of either the law school or the business school admissions office. Get that person’s contact information and get in touch with him or her. Application practices, standards for admission, and specific program structures vary from one school to the next, and your best resource is an expert at that school.
Next, consider what you’ll need to do to get your application package ready. You already know what your B-school application will require; that’s why you’re preparing for the GMAT. But law school applications will require a whole other standardized test, the LSAT. You may not want to deal with that too much while you’re planning for the GMAT, because like the GMAT, the LSAT is a very intense exam. However, the LSAT is only offered 4 times per year, so you’ll need to take that into account when you’re planning your test scheduling. Even if you don’t manage to get a law school application ready in time to apply at the same time you apply for B-school, all is not lost; some schools will allow you to apply for the joint program during your first year.
But how do you even know if you want a joint degree? It’s going to depend a lot on your career goals. Specializing in both degrees will help make you more marketable; if you have a general MBA and a JD with no particular focus, potential employers might see that as an indication that you’re not firmly committed to either business or law careers, and could jump ship from one to the other. However, if you know what kind of work you’d like to do, and can sculpt a program that will be relevant to that, the joint degree can be a big boost. For example, if you’re interested in strategic mergers and acquisitions, labor relations, or consulting, the joint degree will set you apart from the crowd. Even if you choose not to take the bar exam and officially become a lawyer, the legal knowledge that a JD gives you can be a big help in transactional work like contract negotiations.
What else can a JD/MBA give you? Well, as everyone knows, one of the benefits of earning an MBA is the networking opportunities it provides. Your classmates will one day become business contacts, and mutual alumni pride can pave the way for career paths you might not otherwise be able to tread. Earning a JD essentially doubles your professional network, and that can mean valuable opportunities for you.
Now that you’ve considered whether to get a joint degree, and what it might mean for your career, you might be wondering what it would be like to pursue two demanding degrees at the same time.
Look for Part II of this article, when you can hear answers straight from a current JD/MBA student!
For years, scientists have already been telling us that the balanced diet can enhance our overall fitness and well-being. In addition, there are several foods which can be constantly advertised as ‘’brain food’’, in that, they can improve cognitive function and brain health. In case that you’re not familiar with them though, lets go over some of the most well-researched and beneficial ones.
1. Salmon: research shows that Omega-3 fatty acids are essential to cognitive function, and the body cannot manufacture these kinds of fat itself, so you have to get your Omega-3s from food or supplement sources. There are all types of health things to contemplate for various populations, if you’d plan to know more, you can read up on it here. But the main idea is, there’s a large amount of scientific evidence showing that foods loaded in Omega-3 fatty acids truly do feed your brain.
2. Nuts and seeds: foods like flaxseed and walnuts pack identically types of Omega-3 punch that salmon does, and have the extra benefit of providing fiber, which aids to maintain physical health in many means.
3. Blueberries: there’s evidence showing that people who eat a cup of blueberries per day perform 5 to 6% better than a control group does on a test of motor skills. Furthermore, many studies show that the antioxidants in blueberries can help to reverse age-related reductions in cognitive function, such as loss of memory. Plus they create a pretty tasty pie
Now, here’s the vast news: for a few days before taking your GMAT, you might want to move off from your usual healthy diet and indulge a bit. Were not advocating an overall fast food pig-out;you still need to make sure that you get the typical required amounts of nutrients, and don’t overdo it in the calories, as that it can make you sluggish. But a study revealed in September 2009 point out that eating too much high-fat diet for four to seven days before an intellectually strenuous task can have a useful affect performance. The study, titled “Nutritional Effects on Cognitive Performance”, was reported by researchers at the John D. Odegard School of Aerospace Sciences, which is a division to the University of North Dakota at Grand Forks, and produced results which were astonishing to many.
The study tested pilots on a full-motion flight simulator, and also measured their short-term memory. Four varieties of diets were tested: high fat, high carbohydrate, high protein, and balanced. The researchers found that pilots on the high-fat diet constantly out-performed those on the other diets: 27% better than the high protein group and 10% greater than the balanced group, with less essential margins over the high carb group. The high carb group also out-performed the high protein group by 22%, and pilots on the high protein diet reported feeling irritable and having a problem in sleeping.
What does this mean for you? Well, if you’re planning to go to business school, it’s not likely that you’ll be piloting an airplane in the near future. However, most of the cognitive functions used by pilots-short term memory, quick decision-making, and multi-tasking-will are essential to you on the test day. The message here ISN’T to forgo healthy eating for months of carbohydrate and fat-loading. But for a number of days before the test, it may not be a bad idea to have a little extra butter on your bread, and some gravy on your potatoes. After all, every little bit helps.
