Review your answers with detailed explanations and strategies on Grockit.

Question 1: The OLEX Petroleum Company has recently determined that it could cut its refining costs by closing its Grenville refinery and consolidating all refining at its Tasberg refinery. Closing the Grenville refinery, however, would mean the immediate loss of about 1,200 jobs in the Grenville area. Eventually the lives of more than 10,000 people would be seriously disrupted. Therefore, OLEX’s decision, announced yesterday, to keep Grenville open shows that at OLEX social concerns sometimes outweigh the desire for higher profits. Which of the following, if true, most seriously undermines the argument given?

Conclusion: OLEX’s decision to keep Grenville = Social concerns valued over more $$$
Evidence: Refining costs cut by closing Grenville; Grenville closing = loss of jobs/live disruption

Evidence + Assumption = Conclusion

How does the fact that Grenville’s closing would mean loss of jobs necessarily mean that OLEX is socially concerned?

Assumption: The disruption would not lead to less profitability long-term (OLEX is not motivated by greed).

Now we’re going to reverse the assumption, and use it for our Prediction.

Prediction: Disruption = less profitability, OLEX is not concerned w/social well-being and is motivated by greed.

The Prediction should match the correct answer choice as closely as possible. That is why it’s important to write one down whenever possible. When you write down a Prediction, it clarifies for you what you should look for in the answer choices.

A. The Grenville refinery, although it operates at a higher cost than the Tasberg refinery, has nevertheless been moderately profitable for many years.

B. Even though OLEX could consolidate all its refining at the Tasberg plant, doing so at the Grenville plant would not be feasible.

C. The Tasberg refinery is more favorably situated than the Grenville refinery with respect to the major supply routes for raw petroleum.

D. If the Grenville refinery were ever closed and operations at the Tasberg refinery expanded, job openings at Tasberg would to the extent possible be filled with people formerly employed at Grenville.

E. Closure of the Grenville refinery would mean compliance, at enormous cost, with demanding local codes regulating the cleanup of abandoned industrial sites.

The answer here is E. Notice the phrase “at enormous cost”; it shows that OLEX’s motivation is financial and not social. Now try one on your own!

Question 2: The New Deal in America began in 1933 and included widespread bank reforms, unprecedented government infrastructure spending, and unparalleled expansion in the size of government. Some political commentators and economic historians contend that President Franklin Roosevelt’s New Deal singlehandedly propelled the United States out of the Great Depression and into decades of uninterrupted prosperity. To support this claim, these economists note that during the years following 1933, GDP grew, unemployment shrunk, and optimism increased. Which of the following statements, if true, would most weaken the above argument?

A.  The considerable debt burden that the government assumed to fund the New Deal sparked fear in the minds of some economists, investors, and businessmen.

B. The considerable government expenditures and massive labor requirements engendered by America’s entry into World War II in late 1941 helped employ Americans and grow GDP.

C. On average, GDP per capita fell and unemployment rose in many foreign countries during the years after President Roosevelt announced his New Deal.

D. During 1939, the U.S. economy contracted sharply, unemployment jumped 5%, and America’s optimism fell.

E. U.S. GDP during the mid 1930s stood at levels much lower than 30 years later.

Check out the wording of the final sentence before the question. “To support this claim, these economists…” We can translate this as knowing the claim is based on 3 good things that happened after 1933: GDP grew, unemployment shrunk, and optimism increased. What would WEAKEN the argument is that if that evidence, the basis of support for the claim, was taken away.

What would most weaken would be if there were other reasons for (+) outcomes, or if after the New Deal in 1933 things did not continue to get better. Notice how D perfectly matches our prediction. It shows that just 6 years later, things were bad again, contradicting the “decades of uninterrupted prosperity” mentioned in the argument.

Did you choose another answer choice, perhaps B? Let’s examine. Notice how D more directly relates to the specificity of the argument. Since 1939 is earlier than 1941, it would show that the New Deal had even less of an impact. Furthermore, since B produced a positive result, helping Americans and growing GDP, you could argue that so did the New Deal. Who’s to say that it was only America’s entry into WWII that caused the growth? Pre-1941 there could have still been (+) growth, so the argument is not necessarily weakened by choice B.

See other articles in this series:

Anatomy of a Weaken Question – Part 1

Anatomy of a Weaken Question – Part 2

Find out how you can track your progress across specific skills and target your efforts accordingly on Grockit.

Let’s look at the passage and the question we analyzed last time:

Recent U.S. legislation limiting the emissions permissible from automobiles will require auto manufacturers to incorporate new technology and more costly components in cars. This will drive up the price of cars, both at home and abroad. Therefore, the legislation will result in the loss of many export markets.

Conclusion: Legislation = loss of export markets

Evidence: Legislation requires $$ technology; will drive up price of cars

Assump: US cars are more expensive to foreigners; they will stop buying the US cars

Now let’s see how the assumption relates to the answer choices:

The argument to the left is most seriously weakened by which of the following?

A            Most of the countries to which U.S. automobiles are exported have recently enacted similar             legislation limiting emissions.

B            Non-compliance with the new legislation can be punished with high fines.

C            Training factory workers to use the new technology required to manufacture compliant             automobiles will be expensive and time-consuming.

D            Some automobile manufacturers will choose to relocate their plants to other countries that do not             have stringent emissions standards.

E            Environmental groups have been leaning heavily on the auto industry to voluntarily institute such             emissions standards.

This question is weakening “the argument” so we will take the entire argument into consideration here. There are no outside opinions or secondary conclusions we need to worry about. We know the assumptions are NECESSARY to the strength of the argument, and we understand that the underlying assumption here links Legislation à Loss of Export Markets, so the correct answer will make that link invalid. Look for the answer choice that creates a gap between the Legislation and the Loss of Export Markets.

For weaken questions that ask about the entire argument, you can reverse the assumption to make a prediction. If the assumption is something that is necessary, then reversing the assumption will strongly weaken the entire argument.

Prediction: US cars are NOT more expensive to foreigners; they will NOT stop buying US cars

With our Prediction in hand, we can see the correct choice is A. If the legislation has been already enacted, then the US cars will not be more expensive than the foreign cars in the exported countries. Therefore, the conclusion that there will be a loss of export markets is unlikely.

Remember that CR is not based on what you think (or what I think), or on what seems “logical.” It is not an inference. It is based on the ARGUMENT. Don’t start to eliminate or compare answer choices until you have thoroughly broken down the premise. In Part 3 of this series, we’ll look at two harder Weaken questions!

See other articles in this series:

Anatomy of a Weaken Question – Part 1

Try this GMAT critical reasoning question for practice!

Let’s start with the basics – how do you know you’re looking at a Weaken question? Here are some examples of the phrasing you might see on Test Day:

-Which of the following, if true, would most weaken the claim that periodontal disease is a cause of Coronary Artery disease?

-Which of the following, if true, casts the most doubt on the argument to the left?

-Which of the following, if true, most seriously weakens the argument to the left?

Sometimes the word “weaken” will be in the question itself, and sometimes not. The idea is that the answer choices will somehow hurt the passage’s claims.

What is being weakened? Most of the time the entire argument is being weakened, however occasionally only one aspect of the argument is being weakened, or a secondary conclusion. Make sure you know WHAT is being weakened. Otherwise, you risk choosing an answer choice that is weakening the wrong part of the argument!

-Which of the following, if true, most undermines the conclusion stated in the passage to the left?

In this question “the conclusion” is what needs to be weakened, so as you narrow down and compare answer choices, you will need to ask yourself: which choice hurts the conclusion the most? Two answer choices may sound logical, but only ONE will direct its venom more squarely on the conclusion.

In taking apart an argument, you should already be comfortable identifying the Conclusion, the Evidence, and coming up with 2-3 logical Assumptions. You will need to do this before you can answer any weaken question. Let’s refresh on an easy-level Grockit question:

Recent U.S. legislation limiting the emissions permissible from automobiles will require auto manufacturers to incorporate new technology and more costly components in cars. This will drive up the price of cars, both at home and abroad. Therefore, the legislation will result in the loss of many export markets.

Conclusion: Legislation = loss of export markets

Evidence: Legislation requires $$ technology; will drive up price of cars

We know that Evidence + Assumptions = Conclusion, so the assumptions here are anything that will increasingly link the legislation’s requirements to a loss of export markets. Ask yourself: why would the increasing price of cars lead to a loss of export markets? An “export market” means that the US cars are sold overseas. The idea here is that if they are more expensive, then no one overseas will buy them because they will be more expensive than their native automobiles. Here’s how we could write that down in shorthand:

Assump: US cars are more expensive to foreigners; they will stop buying the US cars

Look out for part 2 of this series to see how this Assumption relates to the answer choices in this question! In the meantime, try out some easier Weaken questions in one of Grockit’s group games!

For more GMAT Critical Reasoning advice check out these posts!

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1. Find the Conclusion & the Evidence. Just like you would with any CR, make sure to identify these first.

2. Write down the negation of each answer. It doesn’t have to be a complete sentence; shorthand is efficient and works well.

3. Eliminate choices that do not hurt the Conclusion. You should be able to quickly eliminate at least three of the answer choices.

4. Choose the answer that most specifically relates to the argument. If you are down to two choices, re-read the Evidence and the Conclusion again. Select the one that would have the most negative effect on the argument. Both choices may sound helpful but only one will be essential.

Let’s try a question from Grockit:

The average hourly wage of widget makers in Maltville has been lower than that in neighboring Wineland for at least ten years. Since Wineland and Maltville became a free trade zone five years ago, the number of widgets sold in Wineland has not changed. However, in those five years there has been a decrease in the number of widget makers in Wineland. Therefore, the number of Maltvillian widgets sold in Wineland has increased.

1. Conclusion: – More M-widgets sold in W.

Evidence:  – Fewer makers in W; no. sold in W unchanged

2. Answer choices:

A.  Widgets made in Wineland require more advanced technology to make than do widgets made in Maltville.

Negation: W-widgets do NOT require more tech. than M-widgets.

B.  The number of widget makers in Maltville has increased by exactly as much as the number of widget makers in Wineland has decreased.

Negation: The no. of M-makers has NOT increased at same rate of W-makers decrease.

C.  The number of widgets made annually in Maltville has increased significantly during the past five years.

Negation: No. of M-widgets has NOT increased in past 5 years.

D.  The difference between the hourly wage of widget makers in Maltville and that of widget makers in Wineland is likely to decrease next year.

Negation: Diff. in wages is NOT likely to decrease.

E.  The number of widgets per day a Winelandian widget maker can produce has not increased significantly over the past five years.

Negation: No. of W-widgets per day HAS increased.

3. The focus of the Conclusion is that there are more M-widgets sold in W. Let’s eliminate choices that do not relate to the widget-production specifically: A, B, and D.

4. We are left with two choices: C and E. The author’s argument is that fewer W-makers + same number sold in W = More M-widgets sold in W.

E hurts the argument more significantly than C because it undermines the idea that the widgets are coming from Maltville. If W has enough widgets, then it is likely not importing them from M, and so the conclusion is undercut.

Each sentence has a purpose that builds that structure. Sometimes CR questions will ask what the function is of a part of the argument. You may see questions that ask “which role” a sentence plays. Try to place it into one category: conclusion or evidence? If the sentence was removed from the paragraph, what would be lacking?

Try this GMAT critical reasoning practice question and see if you’re ready for test day!

Paraphrase the argument. Dumb down the complexity of the argument as you read, as if you were explaining it to a child. You may want to write down a few short notes to help you. The idea is to ignore the petty details and see through to the author’s main point and to the evidence he provides to support his point.

Choose a verb. Questions about argument structure often ask about the “methods” an author uses. You already know the flow of the overall argument, now give it an overall purpose and label as an infinitive verb. Common verbs:

Look for transitions. Transition words and phrases are like signposts pointing your way through the logic of the argument. They tell you what is coming next. “Specifically…” means a more detailed example will follow. “Thus,” means a summation is to be expected. “While this may be true…” is a phrase that shows a concession is about to be made. Keep a study sheet of transition words and divide them into categories: Examples, Adding, Contrasting, Emphasis, Resulting In, etc. It’s an ongoing process to familiarize yourself with these, but a worthwhile one.

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What are they? Resolve the argument questions ask about a specific incongruous aspect of the argument.

How to identify? Look for some common keywords such as: “explains the results,” “resolve the paradox,” “best explains the discrepancy,” etc. Unlike other CR questions, these don’t ask how to weaken or strengthen the argument itself.

How to approach? Like any other CR question, you’ll want to identify the conclusion, evidence, and assumptions before even reading the question. Once you realize it’s a “Resolve the Argument” question, you’ll want to rephrase the question in simpler terms, then go back to the passage and find what the “paradox,” “results,” or “discrepancy” is describing. Specifically, pay attention to what is lacking in the details. Usually the author fails to provide enough information. If you were to make the same argument, what would you add to resolve the issue brought up in the question? Write down your prediction(s) then scan the answer choices, eliminating those that do not resemble your prediction.

For quick reference:

1. Identify the conclusion, evidence & assumptions.
2. Read and rephrase the question.
3. Go back to the passage & form a prediction.
4. Eliminate incorrect choices.

Let’s try out a Resolve the Argument question from Grockit’s CR question bank:

The majority of a person’s health care expenditures goes towards curative measures like hospitalizations after injuries and care for existing illnesses. Paula’s employer does not provide health insurance to his part-time employees, including Paula. However, he does reimburse employees for a flu shot each winter.

Paula’s employer’s seemingly inconsistent behavior in regard to health care expenses is best explained by which of the following?

A. Health insurance rarely covers pre-existing illnesses.

B. Part-time employees are usually covered by the insurance of a spouse or parent with full-time employment.

C. Few employers offer health insurance to part-time employees.

D. Flu shots prevent illness that could lead to lost work days.

E. Health insurance premiums are on the rise.

Conclusion: Paula’s employer does NOT provide health insurance to part-timers.

Evidence: Majority of $$ goes towards curative measures (fixing injuries, illnesses); reimburses for flu shots.

We can see the gap in logic here. Why would an employer who doesn’t pay health insurance reimburse employees for a flu shot?

Assumption: The employer sees some $$ benefit in paying the flu shot (a preventative measure), even though he won’t pay health insurance. He doesn’t want his employees to get sick in the first place.

We can see this is a “Resolve the Argument” question because of the phrase in the question stem, “best explained.”  So let’s rephrase the question and predict what the answer choice might involve.

Question Rephrase: What’s the strongest reason why the employer would pay for a flu shot but NOT pay health insurance?

Prediction: Some unknown benefit to the employer in the long-term.

Since we’ve done the work of breaking down the passage, simplifying the question, and predicting an answer, the correct choice (D) is readily apparent. To practice more Resolve the Argument questions, you can create a Custom Game on Grockit using only those CR questions with the “Resolve Argument” skill tag.

2. Determine what is missing. What does the blank represent? Often it will be either a restatement of the conclusion,  or another supporting piece of evidence, but it could also be an action advocating by the author, or an example of the author’s argument applied to the real world.

Try this GMAT critical reasoning practice question and test your GMAT skills today!

3. Make a prediction (and write it down)! This is the most important step. Come up with a logical phrase for the blank, in your own words, based on what you think the blank represents to the argument as a whole. If you’ve determined the blank is the conclusion, come up with your own logical conclusion based on the evidence. If you believe it’s something the author is advocating as a next step, try to consider his perspective and come up with a reasonable leap. Don’t worry about making it perfect – just get something down on paper!

4. Eliminate out-of-scope answers. While the correct answer may not perfectly match your prediction, the simple fact that you took the time to think critically while you came up with a prediction will help you understand the author’s focus and the flow of his argument. Eliminate answer choices that would NOT follow the gist of the paragraph. Especially look for those that are outside the scope of the author’s focus, a favorite CR wrong answer type!

Sample Question:

Old, longstanding firms concentrate on protecting what they have already amassed. Consequently, they rarely innovate and often underestimate what consequences innovation by other companies will have. The best example of one such defensive strategy is the fact that ___.

Which of the following best completes the passage?

Our Notes:

Conclusion – Old firms don’t innovate & underestimate other companies that do.

Evidence – Old firms concentrate on protecting what they have.

Assumptions – Protecting what you have = NOT innovating

What’s the blank represent? An example that will prove the author’s point.

Prediction: An old firm that didn’t innovate & suffered as a result of another company that did.

Answer Choices:

A.   electronics and mass-produced gears eliminated the traditional market for pocket watches, clearing the way for marketing them as elegant, old-fashioned luxury items.

Incorrect. This is contradictory since the traditional pocket watch makers changed their marketing (and thus innovated.)

B.   an extremely popular prefabricated house was introduced by a company that, several years before, had failed miserably with its product line of glass houses.

Incorrect. This is contradictory since it shows a company that innovated.

C.   a once-leading maker of buggy whips responds to the new availability of stick shifts by attempting to make better buggy whips.

Correct! Here an old buggy whip firm does not innovate and simply focuses on what they already have.

D.   smoking pipes, originally designed for use by typically older, more traditional smokers of tobacco, are now bought mostly by young smokers of scented or flavored herbal blends.

Incorrect. This focuses on the consumer. We would consider this “out of scope” since our argument focuses on the producers.

E.   the psychiatrist who invented the anti-inhibition drug MDM did not mean for his product to be used by partygoers, who buy most of the drug now called “Ecstasy.”

Incorrect. This focuses on the intentions of the producer, which is also “out of scope” to our argument.

Study online any time of the day, from anywhere you have Internet access on Grockit today.

The questions themselves aren’t all that different from most of what you’ll see on the test: there’s a plan (or argument, in some cases), and the question stem asks you to identify the information that would be most helpful in evaluating the plan.  This can take different forms; sometimes you’ll be asked to choose a study or research topic, for example, and other times you’ll be asked to identify the question that, when answered, would help you to evaluate the validity of the plan.  The key to answering Evaluate the Plan questions with a minimum of stress is to use the skills that you employ for Assumption, Strengthen, Weaken, and some Flaw questions: look for a gap in the reasoning.

For example, an assumption question might look like this:

Video game designers develop innovative new gaming technology in response to the demands of the market.  Only serious gamers are willing genuinely interested in innovative technology and willing to pay for it.  Therefore, the video game designers at XYZ Gaming Corp. will develop new gaming technology only if it can be used in violent car-chase video games.

Which of the following is an assumption…

The correct assumption for this question would be something like this:

Serious gamers are only interested in innovative technology that can be used in violent car-chase video games.

This assumption ties together the evidence, which discusses serious gamers, with the plan, which addresses violent car-chase video games.  But the same stimulus could be used for an Evaluate the Plan question, and the same identification of the gap in the reasoning could help us choose the correct answer.  Let’s look at the question again, from that perspective:

Video game designers develop innovative new gaming technology in response to the demands of the market.  Only serious gamers are willing genuinely interested in innovative technology and willing to pay for it.  Therefore, the video game designers at XYZ Gaming Corp. will develop new gaming technology only if it can be used in violent car-chase video games.

The answer to which of the following questions would be most useful in evaluating the validity of XYZ Gaming Corp.’s plan?

1. a. Are violent car-chase video games popular with the “casual gamer” segment of the market?
2. b. What percentage of serious gamers is willing to invest significant amounts of money in purchasing newly developed technology?
3. c. Are serious gamers interested in innovative technology that can be used in games outside of the violent car-chase genre?
4. d. On average, what percentage of the total annual video game market has been comprised of violent car-chase video games for each of the last five years?
5. e. How would one distinguish between a serious gamer and a casual gamer?

We know from evaluating this as an assumption question that there’s a gap between serious gamers and violent car-chase video games; now we look for a question that, if answered, would allow us to determine whether or not the link between them exists.  We find that in choice C.  If the answer to C is ‘yes,’ then the assumption we identified earlier is invalid and the plan is not a solid one.  If the answer is ‘no,’ then the plan is valid.  Either way, though, the answer to the question in choice C is important in evaluating the plan.

The basic approach for Evaluate the Plan questions, then, is similar to what you’ve been doing for assumption questions; you just need to take an extra step beyond identifying the gap to finding the question or study that would help you to fill it.

1. to derive by reasoning; conclude or judge from premises or evidence: e.g., They inferred his anger from his heated denial.

2. (of facts, circumstances, statements, etc.) to indicate or involve as a conclusion; lead to.

3. to guess; speculate; surmise.

4. to hint; imply; suggest.

“Infer” is, as you can see, a word with fairly flexible meaning.  We most often use it in day-to-day life to mean “make an educated guess.”  If your friend Jane says she doesn’t eat hot fudge sundaes, you apply your existing knowledge about the possible reasons someone could have for not enjoying the hot fudge and ice cream deliciousness, and you make an educated guess as to what her reasons could be.  On the GMAT, however, “inference” has a different meaning.  Think of inferring as the process of deriving the strict logical consequences of assumed premises.

On the GMAT, therefore, if you are told that Jane doesn’t eat hot fudge sundaes, you can derive two logical consequences from that premise:

1. If Jane is eating, has eaten, or will eat something, it isn’t a hot fudge sundae, and
2. If someone is eating, has eaten, or will eat a hot fudge sundae, that person is not Jane.

The correct answer to an inference question on the GMAT will follow directly from the evidence provided; it is NOT merely an educated guess, but is instead the logical consequence of the assumed premises.

Notice that just based on six words—“Jane doesn’t eat hot fudge sundaes”—we can draw two possible inferences.  Now think of how many words you might see in the average GMAT question, and you’ll understand that inference questions, unlike other types of questions, don’t lend themselves well to prediction.  Trying to guess the correct inference being drawn from several sentences worth of statements is generally a waste of time.  Your best bet in approaching GMAT questions that ask for inferences is to use process of elimination, just as you would in sentence correction.  Eliminate answers that are just “educated guesses,” answers that aren’t necessarily true, answers that are too extreme, and of course, anything irrelevant.  Your answer will be the one choice that follows strictly from the statements in the question.

Let’s look at a sample GMAT-type question:

XYZ Corporation has two divisions, both of which performed consistently over the last five years.  The Interment Services Division accounted for approximately 30% of the corporation’s transactions and 50% of the corporation’s profits; the Toxic Household Products Division accounts for the balance.

The statements above support which of the following inferences about XYZ Corporation over the last five years?

1. Measured in dollars, the total profits for XYZ Corporation have remained stable over the last five years.
2. Interment Services is an increasingly competitive field, while Toxic Household Products are a largely untapped market.
3. The Toxic Household Products Division yields a lower average profit per transaction than does the Interment Services Division.
4. XYZ Corporation’s Toxic Household Products line has remained consistent over the past five years.
5. Most families will, over a given five-year period, spend more money on Interment Services than on Toxic Household Products.

Only one of these answer choices MUST be true; let’s take a look at the options:

1. We only know about percentages, or proportions, so we can’t draw inferences about dollar amounts.
2. No information is provided about competition for either Interment Services or Toxic Household Products.
3. This is the correct choice; Interment Services has a profit to transactions ratio of 50%:30%, or 5:3, while Toxic Household Products has a ratio of 50%:70%, or 5:7.  Therefore, the Toxic Household Products Division is doing more than twice as many transactions as the Interment Services Division, but yielding the same profits.
4. Product lines are not discussed, and therefore can’t be the subject of an inference.
5. Per-family spending is never mentioned, so we can’t infer anything about it.

There’s a pattern here: if it’s not mentioned, an inference can’t be drawn about it.  Inferences MUST be supported by the evidence provided; remembering this one concept will give you a solid start in conquering inference questions on the GMAT.

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:

Try this GMAT critical reasoning question for more practice!

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:

1. When forming a contrapositive, turn “and” into “or” and vice versa.
2. “Neither X nor Y” means “No X and no Y.”
3. “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!