There are two different prices, $10 and $25, for tickets to a play, and a total of 100 tickets were sold. The question asks whether more adult tickets were sold than children's tickets.

Glance at the statements. They both involve "overall" numbers—average revenue per ticket and total revenue. This is a weighted average question in disguise. If more adult tickets were sold, then the average ticket price will be closer to $25 (the price for one adult ticket). If more children’s tickets were sold, then the average ticket price will be closer to $10 (the price for one children's ticket).

(1) SUFFICIENT: $18.25 is closer to $25 than to $10, so more $25 tickets must have been sold. That is, Yes, more adult tickets were sold than children's tickets.

(2) SUFFICIENT: The total revenue from ticket sales exceeded $1,800. How are ticket sales calculated? look at the information in the question stem again. One hundred tickets were sold. Consider two extreme scenarios:
Scenario #1: 100 children's tickets were sold. In this case, revenue would be (100)($10) = $1,000.
Scenario #2: 100 adult tickets were sold. In this case, revenue would be (100)($25) = $2,500.

What if there were exactly 50 children's tickets and exactly 50 adult tickets sold? The revenue from children's tickets would be half of $1,000, or $500. And the revenue from adult tickets would be half of $2,500, or $1,250. Total revenue would be $500 + $1,250 = $1,750.

Statement (2) indicates that revenue was actually greater than $1,800, so Yes, more adult tickets must have been sold.

The correct answer is (D): Either statement by itself is sufficient to answer the question.

The question provides some facts and then asks which answer choice must be true. You'll need to Test Cases on this one: Try some real values that are consistent with the facts and test the answer choices, crossing off anything that's False. Repeat the process until you have only one answer choice left.

The value of a is negative, and b must be less than c (but they could be positive, negative, or zero). When testing cases, it can be really fast to choose 0 if allowed. You can choose either b = 0 or c = 0; see whether that knocks out any answers quickly.

If b = 0, then answer (C) can't be true, because 0 is not greater than 0. Likewise, if c = 0, then answer (D) can't be true, because 0 is not greater than 0. Eliminate answers (C) and (D).

The remaining answers are more complicated. If a = –1, b = 1, and c = 2, then:
(A) ab < c becomes –1 < 2, which is True
(B) ac > b becomes –2 > 1, which is False so eliminate (B)
(E) ab > ac becomes –1 > –2, which is True

Answers (A) and (E) are still in the running. How can you change the types of numbers that you tried the first time? The value of a must stay negative, but b and c don't have to stay positive. Try negative values to see what happens.

If a = –1, b = –3, and c = –2 (remember, b has to be less than c!), then:
(A) ab < c becomes 3 < 2, which is False, so eliminate (A)
(E) ab > ac becomes 3 > 2, which is True, so (E) is the correct answer!

The story is complicated, so take your time in understanding what it says. Company X has just these two product lines, so you don't need to worry about any other possible sources of revenue.

From 2014 to 2015, the consumer product line (C) increased revenues by k% and the machine parts line (M) decreased revenues by k%. The question asks whether the company's overall revenues increased in 2015.

At first glance, it might seem like you need to know how much revenue each product line made, as well as by what percentage the revenues increased or decreased in 2015. But the fact that the two percent changes are the same value, k, makes a big difference in how this problem can be solved.

Imagine that k = 10. In this case, Line C's revenues increased 10% while Line M's revenues decreased 10%. If they both had $100 in sales in 2014, then Line C would have sold $10 more in 2015 and Line M would have sold $10 less in 2015, so overall revenues would have stayed the same.

What if Line C's revenues were $1,000 in 2015 and Line M's revenues were only $10? In that case, Line C's 10% increase would represent a lot more revenue gained than Line M's 10% decrease would represent revenue lost, so Company X would have earned more revenue overall in 2015. Conversely, if Line C's revenues were $10 in 2015 and Line M's revenues were $1,000, then Line M's 10% decrease would overwhelm Line C's 10% increase, and so Company X would have earned less revenue overall in 2015.

In other words, in order to know whether Company X earned more revenue in 2015, you really need to know which line earned more money in 2015: Line C or Line M. It doesn't matter whether the value of k is 1% or 10% or 87%, since k is going to be the same percentage for both calculations.

(1) SUFFICIENT: This statement indicates that Line C generated more revenue than Line M in 2014. Since this was the case, Line C would represent more of a gain in annual revenue in 2015 than Line M would represent a loss, so the answer to the question is a definitive Yes, Company X earned more revenue in 2015 than it did in 2014.

(2) INSUFFICIENT. As shown earlier, the exact value of k does not tell you anything about whether Company X earned more in 2015. You need to know something about the revenues of each business line in order to conclude anything about overall revenues.

The correct answer is (A): Statement (1) by itself is sufficient to answer the question.

This is a really complicated rate problem—but there are two "neat" solutions that can save you a lot of time. First, just note the trap in the question. It asks you to reduce the time needed by 2 days—that is, to take 6 days for the job rather than 8 days. The test writer is hoping you'll misread that and think that the whole job should be done in just 2 days, not reduced by 2 days.

The first, and fastest, approach works if you can train yourself to "logic it out." (And, if it helps, draw it out as you go.) The 12 machines can do the entire job in 8 days. The question asks how many extra machines you'll need in order to finish the whole job in just 6 days.

If 12 machines do 100% of the job in 8 days, imagine what will happen if you turn the machines off after 6 days. What percentage of the job will they have completed? Since 6 out of 8 days is 75% of the total time, the machines will have completed 75% of the total job.

So, in 6 days, your original 12 machines will have completed 75% of the job, leaving 25% unfinished. How many more machines will you need in order to do 25% of the job over that 6-day period?

The key is in noticing that 25% of the job is one-third of 75% of the job—and you already know how many machines you need for 75% of the job. If 12 machines can do 75% of the job in 6 days, then one-third of 12 machines (= 4 machines) can do one-third of 75% (= 25%) of the job in 6 days.

So you need 4 extra machines if you're going to reduce the total time for the job by 2 days.

The correct answer is (C).

It's worth trying to learn to train your brain to logic this out because this is exactly the kind of logical-thinking-about-quant that will be useful in the real world when you're at work. But you can also try algebra.

Your unknown is r, the rate at which one machine works. Initially, the rate for 12 machines is 12r, the time is 8 days, and the work done is 1 job: (12r)(8) = 1 job.

In the new scenario, you don't know how many machines you'll have, so call that n. The rate for n machines is nr, the time is 6 days, and the work done is 1 job: (nr)(6) = 1 job.

Set the equations equal to each other and solve:
(12r)(8) = (nr)(6)
[(12)(8)] / 6 = nr / r
(2)(8) = n
16 = n

The new number of machines is 16, so the extra number of machines needed is 16 – 12 = 4. The correct answer is (C).

Identify the Question: The question stem asks for something that is required for the student advisor to draw this conclusion. Premises that are necessary but unstated are called assumptions; this is a Find the Assumption question.

Deconstruct the Argument: A student is having arguments with her parents. Also, over the same time period, the student’s GPA has gone down. The advisor concludes that there is a causal relationship: that the family problems caused the academic problems. Maybe the causation is reversed, or maybe the two are unrelated?

Pause and State the Goal: The conclusion is about a causal relationship between two things. In such an argument, there is an assumption that the two things are not related in some other way. Find an answer choice that rules out other explanations!

Work from Wrong to Right:

(A) This works against the advisor’s conclusion by suggesting a different reason for the GPA dip. Answer choices like this can be tempting because they reveal the assumption—that there are no other possible explanations—but they do so by working against it. Revealing the assumption is not the same as stating it!

(B) CORRECT. This answer choice seems to reject the notion that the causation is reversed; in other words, it rules out another explanation. Try negating this. If the student’s GPA went down first and her parents got mad at her as a result, then the advisor couldn't claim that the family problems caused the lower GPA. The argument falls apart.

(C) This answer choice defends the idea that the argument at hand matters by suggesting that GPA is something worth caring about. Your job is to find the assumption of the student advisor’s argument, whether or not that argument is an important one to have.

(D) This is an irrelevant distinction. The argument deals with explaining a decrease in a student's GPA from its previous level, not from a schoolwide average. Regardless of how her GPA measures up, it recently fell, and this advisor is attempting to explain why.

(E) Saying that something is common is not the same as explaining its cause! This choice works against the advisor’s conclusion that the problematic family relationship caused the student’s difficulties. It suggests instead that the student’s GPA decrease was simply a random fluctuation.

Identify the Question: The words if true and weaken indicate that this is a Weaken the Argument question.

Deconstruct the Argument: There's a plan to double the capacity and costs of the theatre. The theatre is only a little profitable now, the population of the town isn't expected to increase, and it seems like the town has mostly tapped out its customer base. The author concludes that the expansion plan will end up being unprofitable for the theatre.

And it doesn't sound like the greatest plan! Profits equal revenue minus cost. Costs are going to go up, but even though theatre capacity is going to go up, it's not clear that more people will actually come (that is, that revenues will actually increase).

Pause and State the Goal: The question asks you to weaken the argument. The conclusion is that the plan will be unprofitable, so what new information might actually turn the plan around and give the theatre a better chance to be profitable?

Work From Wrong to Right:
(A) If anything, another option for entertainment would threaten the theatre's revenues, not help. This choice does the opposite of what was asked: It makes it more likely that the author of the argument is correct that the theatre will not be profitable.
(B) It's not clear whether the food-and-drink portion of the business model is currently profitable or unprofitable. If the food and drinks are very profitable, then it could be a good thing to have more theatre capacity—also assuming that more people actually attend. But if the food and drinks aren't profitable (perhaps they're a loss-leader?), then selling more of them will make it less likely that the theatre will turn a profit. There's not enough information given to know how this choice affects the argument.
(C) If more people are moving to town, they could be potential new customers for the theatre...except that this choice says that they're *not* as likely as other people in town to attend the theatre. So there's no new information in this choice to make it more likely that the theatre's plan might allow it to be profitable.
(D) CORRECT. The argument established that costs would increase but did not establish that revenues had a chance to increase as well. This choice establishes that the theatre may be able to increase its customer base—a definite increase in revenue at least for ticket sales (and possibly for other things, such as food and drink). This makes it more likely that the plan could be profitable, weakening the author's argument that the expansion would prove unprofitable.
(E) It's not clear how this information might impact profitability, revenues, or costs.

Identify the Question: The question asks you to support one of the following conclusions, that is, one of the answer choices. This indicates that the conclusion is in the answer choices—this is an Inference question.

Deconstruct the Argument: A certain museum has two requirements in order to display a work of art: It has to be proven to be authentic and it can't be damaged. A certain vase currently in the museum might not be authentic, but the only way to check would be to pulverize part of the vase in order to examine it.

Pause and State the Goal: On Inference questions, the goal is to find the choice that must be true given the information presented in the argument. What can you conclude definitively from the given facts?

Work From Wrong to Right:
(A) It's certainly possible that an object displayed in a museum is both valuable and rare, but that isn't necessarily true for every object displayed in a museum. The argument does not provide any evidence that Mycenaean vases in particular are always both valuable and rare.
(B) This choice is tempting, but the argument does not say that the vase in question is definitely a fake, only that some doubts have been raised. If the vase is authentic, then the museum did properly establish its authenticity. And even if the vase is fake, that doesn't mean that the museum was not sufficiently diligent; the vase could just be an exceptionally good fake.
(C) CORRECT. The museum only displays authentic objects that are undamaged. If they do the test and discover the vase is a fake, they'll no longer display it. If, on the other hand, the vase is authentic, they will have had to damage it in order to prove that it's real. Since they don't display damaged objects, they'll no longer display the vase.
(D) The argument indicates that spectroscopic analysis is one possible method to establish the authenticity of objects, but it does not say that it is the only method used by this museum.
(E) This is likely true in the real world, but the argument does not provide any information to support this claim.

Identify the Question: The language logically concluded from the passage above indicates that this is an Inference question.

Deconstruct the Argument: The prompt contains some stats about China and France, related to their World Bank voting shares and their shares of world GDP. It will be important to keep all of these numbers straight.

Pause and State the Goal: This is an Inference question, so you need to find something that must be true based upon the prompt. Stated differently, you need to eliminate every choice that can be false. Basically, the prompt says that China has a larger share of the world GDP than France and that China used to have a lower voting share than France, but now it has a higher share.

Work from Wrong to Right:

(A) Given what you already know, can this be false? Yes! Only GDP data for 2010 is presented. Anything could have been true about China’s share of world GDP prior to 2010.

(B) CORRECT. Given what you already know, can this be false? If they were directly proportional, a country with more than twice the GDP of another would also have more than twice the voting share. China’s share of world GDP is more than twice France’s, but its voting share is almost the same. The voting share cannot be directly proportional!

(C) Given what you already know, can this be false? Yes! China’s share was higher in 2010, but the prompt says nothing about whether these shares were changing, let alone at what rate. Anything could be true about the rates that the shares of world GDP were changing in 2010.

(D) Given what you already know, can this be false? Yes! There’s no way to know this using only the information in the prompt. Nothing can be concluded about the Chinese government if no information about the Chinese government is provided.

(E) Given what you already know, could this be false? Yes! One could speculate that this was true but would not be able to prove it. This answer choice, if true, would aid in an understanding of the facts, but it’s not the only possible explanation. Voting shares could be random! Nothing in the prompt prevents that.

Identify the Question: The boldface font indicates that this is a Describe the Role (aka boldface) question.

Deconstruct the Argument: Boldface arguments tend to be complex, so take your time. A media critic is making an argument. Network TV executives think that other devices and platforms are eating into their market share and they claim, in the first boldface, that this will hurt their ad revenue and they'll no longer be able to spend as much to produce high-quality programming—which will just help to further reduce TV viewership. But the media critic disagrees, citing research in the second boldface that says people using alternative platforms are actually increasing how much TV they watch each week. So, the critic concludes, network TV executives will not lose out on ad revenue because people are also watching TV on other platforms.

Pause and State the Goal: On boldface questions, your goal is to articulate the role that a boldface statement plays in the overall argument. In this case, the first boldface represents a claim made by the network TV executives, with whom the media critic disagrees. The second boldface is a fact—a piece of evidence—used by the media critic to make a competing argument.

Work From Wrong to Right:
(A) It's true that the first boldface goes against the critic's claim, but it is not a trend (or fact); rather, it is a claim made by the TV executives. The second boldface is not the critic's claim; rather it is a fact used by the critic to support the critic's claim.
(B) CORRECT. The first boldface is indeed a prediction, or claim, that the critic challenges. The second boldface is a finding, or fact, used to support the critic's argument.
(C) The first boldface is not reasoning used by the critic; it is reasoning put forth by the TV executives, with whom the critic disagrees. The second boldface is used to support the critic's claim, not to show that the critic's claim is flawed.
(D) The first boldface is indeed something that the network executives believe will occur (though the critic disagrees), but the second boldface is not a consequence of the TV executives' position. Rather, the second boldface supports the critic's argument.
(E) The first boldface is indeed the opposite of the critic's claim. But the second boldface is a fact that supports the critic's claim, not something that shows the critic's claim won't hold.