1. C Rather than multiply out each side of the equation, let’s simplify. We can rewrite 16 as 24. If we cancel 23 from each side of the equation, we are left with 2(3)2 = x. The correct answer is C, 18.
2. C Statement (1) tells us the reduction as a percentage, but without a dollar figure we don’t know the exact amount of the reduction. We are left with B, C, and E.
Looking at Statement (2), we now know the dollar amount after the reduction, but without knowing either the original amount, or the percentage of the reduction, we don’t know enough to answer the question. Eliminate B and only C and E remain.
However, when we put the two statements together, we have enough information to write an equation: 0.75x = $36, where x is the original amount. Once we subtract the price after the reduction, we’ll have answered the question. But remember, for Data Sufficiency questions, we don’t need to get the actual answer to the question; we just need to know that we can. The correct answer is choice C.
3. B This is a percent problem, so let’s start by finding the number of players who traveled more than 200 miles: 65% of 720 is 468. The number of players who traveled 200 miles or less, then, is 720 – 468 = 252 (or, alternatively, 35% of 720 is 252). Although both 468 and 252 are answer choices, the question asks for the difference between the two types of participants: 468 – 252 = 216.
If you’d prefer, you can also deal with the difference of the percentages rather than that of the actual numbers of people: 65% – 35% = 30% and 30% of 720 is 216.
4. D Joe Bloggs might be tempted by B on this yes-or-no data sufficiency problem, because Statement (2) certainly does answer the question. But take another look at Statement (1). If r = 4s, then we can substitute 4s for r in the first equation, making it 4s – s = 240, or 3s = 240, which means s equals 80, and r equals 320.
5. A Any problem with terms like “speed” or “miles per hour” can typically be solved with the formula: distance = rate × time. This problem asks for the speed, or rate, which means distance divided by time. 7 divided by 1
, which is 1 hour and 10 minutes written as a mixed number, equals 6.
6. A The question tells us that Bob purchases a total of 18 cans of soda. Statement (1) tells us there is an equal number of diet and non-diet cans. This answers the question so our choices left are A and D.
Statement (2) may seem to agree with Statement (1) because we may have noticed that the number of diet cans supplied by the information in Statement (1) happens to be odd. However, there are lots of odd numbers. The correct answer is A.
7. E The variables in the answer choices indicate this is a Plugging In problem, but the word “must” means you may have to plug in twice to be sure you have the correct answer. Because y must be an odd integer, let’s use 3. Now, all we have to do is plug 3 into each of the answer choices. Any choice that does not yield an even integer can be crossed off immediately. If more than one of the choices yields an even integer, we will have to plug in a second number for y to see which choice always yields an even integer. Using 3 as our value for y, we find that choices A, B, C, and D all yield odd integers, and E produces an even integer. Therefore, the correct answer is E.
8. D This is a ratio problem, so set up the ratio box. We need to add the “parts” of our ratio to get the “whole” required to form a fraction. Since our parts are 3 and 8, our whole is 11; the total number of students is 220, so 220 divided by 11 is 20, which means we need to multiply all the numbers by 20. 8 students participate in neither program, so 8 multiplied by 20 is 160. The correct answer is D.
Be careful not to choose B, the number of students who do participate in one of the programs, or C, the difference between the number of students who participate and the number who don’t. Judicious use of POE might have eliminated both answers, though, along with A: Since we know that more than half of the students do not participate in either program, we can eliminate any answer less than 110.
9. C To help understand this question, try plugging in some values. Statement (1) tells us that point (x, z) lies in quadrant I, which means that x and z must both be positive. For example, let’s say (x, z) is (3, 4). We know x is positive, but does this tell us anything about y? Nope, so only answer choices B, C, and E remain.
Statement (2) tells us that point (w, y) lies in quadrant III, which means that w and y must both be negative. For example, let’s say (w, y) is (–2, –5). In this case, we know y must be negative, but does this tell us anything about x? Nope, so we are left with answer choices C or E.
If we put the two statements together, we know x must be positive and we know y must be negative—for example, using the points we plugged in, (x, y) is (3, –5)—which means point (x, y) must be in quadrant IV. The answer is C.
10. D Laura pays back 2.5 percent of the loan each quarter of the year. 2.5% of $240 is $6.00. If she has already paid $42.00, that means she has paid that $6.00 for seven quarters. To pay back $42.00 requires 7 quarterly payments. How many months is that? Each quarter of the year is 3 months. The correct answer is D.
11. A To solve this yes-or-no question, plug values into the two statements. To be a factor of 12, the product of xy must be equal to 1, 2, 3, 4, 6, or 12. Let’s make x equal 2 and y equal 3. Is x a factor of 12? Yes. In fact, as long as xy must be a factor of 12 and x and y are integers, x must ALWAYS be a factor of 12. Only answer choices A and D remain.
Now, let’s look at Statement (2). The fact that y = 3 does not help us to know whether x is a factor of 12. The answer is A. Joe Bloggs might have been tempted by C because he’d have a definitive value for x.
12. E Statement (1) only tells us the time it takes the zebra to reach the stream from its current position; since it gives us no information about the time required to reach the pond, Statement (1) is insufficient alone, and we’re down to B, C, or E.
Similarly, since Statement (2) only tells us the time it takes the zebra to get from the pond to the stream—and doesn’t mention the zebra’s current position—Statement (2) is insufficient alone, and we’re down to C or E.
Be careful when you combine the two statements: Although it may be tempting to simply add our travel time and calculate that it takes the zebra 4 hours to go from its current position to the pond, this is only true if all 3 locations were in a straight line, so that the pond would be directly on the other side of the stream. We, of course, can’t assume that to be the case. For instance, if the zebra travels 2 hours due west from its current position to the stream, and then travels 2 hours due east from the stream to the pond, the zebra’s current location would be at the pond! The correct answer to this question is E.
13. A Joe Bloggs wants to pick answer C because he knows that x2 – y2 = (x + y)(x – y) and he figures he will need both statements to give him the answer. But if (x – y) = 0, then what (x + y) equals is irrelevant because zero times any number equals zero.
14. C As always, when there are variables in the answer choices, the easiest thing to do is plug in. If you always get a remainder of 2 when you divide x by 5, then x is some multiple of 5 plus 2 more. In other words, x could be 7 or 12 or 17 or 22, etc. Now, we have to go through the answer choices Plugging In numbers for x that allow them to be integers as well. For example, in A, if we plugged in 17 for x, that gives us 
, which is an integer. Cross off choice A. In choice B, if we plugged in 22, we get 
which is an integer. Cross off B. In D and E, Plugging In the number 12 makes both choices integers. Only choice C is never an integer as long as x divided by 5 has a remainder of 2. The correct answer is C.
15. E When you see variables in the answer choices, the best way to solve the problem is to plug in. Because the total number of pounds of meat is 7, it makes sense to choose numbers that are divisible by 7. Choosing $14 for x and $7 for y, we end up with $9 per pound for the mixture. Plugging our values for x and y into the answer choices, only one gives us $9: E.
16. A To solve this yes-or-no question, plug values into the two statements. Joe Bloggs liked Statement (2) because he forgot that y could equal –
. However, only Statement (1) answered the question. Square roots are always positive. The correct answer is A.
17. B To solve this yes-or-no question, try plugging values into the statements. Looking first at Statement (1), we know that b = 3. If we plug in 2 for a, we get a “no” answer to the question “is the product ab odd.” If we plug in 5 for a, we get a “yes” answer, so we are left with B, C, and E as the potential answer choices.
Now, Plugging In for Statement (2), we eventually realize that if a and b are consecutive integers, one of them must always be even, and the other odd. And the product of even times odd is always even. So Statement (2) answers this yes-or-no question with a resounding “No.” Joe Bloggs was probably tempted by C, but if you plug in enough in this question, you will notice that Statement (2) is sufficient.
18. D To find this average, draw an average pie and realize you have to divide the total number of sales by the total number of months. The total sales for the first year were 12 times 42 or 504. The total sales for the first 10 months of this year were 10 times 20 or 200. So the average number of sales per month is found by dividing the total number of sales, 704, by the total number of months, 22. The answer is 32. Note that A and E are completely out of the ballpark. Because there were more months for which the sales averaged 42 than for which they averaged 20, the correct answer is bound to be a little more than the average of the two averages, 31. Choice C, 31, is the Joe Bloggs answer; Joe loves to take an average of two averages.
19. D First, draw the picture. It looks something like this:
The problem states that AB is the diameter of the circle and that X is center of the circle. Note that point C lies closer to point A than to point B but if you miss that subtlety, you can still get the problem correct. ABC is the triangle that connects the 3 points. AC and AX can be labeled 3—as can BX, since, like AX, it’s a radius.
We already have 2 of the 3 sides we need to find the perimeter of the triangle! To find the 3rd side, we’ll need to know a geometry fact that is only infrequently tested by the GMAT: Triangle ABC, because it’s inscribed in a semi-circle, is a right triangle, with the right angle being at point C. Now we can use the Pythagorean theorem—or, even better, recognize ABC as a 30–60–90 triangle—to determine that BC is 3
. Our perimeter is thus 6 + 3 + 3, or 9 + 3. The correct answer is D.
Be careful not to fall for any trap answers: A is the area of triangle ABC; B and C are the perimeters of the 2 smaller triangles.
20. D If we add up what this passenger actually paid, $1,050, plus the $210 she saved, we get what the purchase price would have been the following day, or $1,260. Now, according to the table, if she had purchased her ticket 6 days before the flight, she would not have saved any money at all, so we can eliminate A. If she bought the ticket 7 days before, she would have saved 10%. Does 10% of $1,260 equal $210? No, so eliminate B. If she purchased her ticket 13 days before the flight, she would not have saved any more money than if she had bought it the next day (12 days before the flight) so we can eliminate choice C. Let’s assume she bought the ticket 14 days in advance of the flight for $1,050, which is a $210 saving from what the ticket would have cost her the day after. That means the ticket would have cost $1,260 from days 13 through 7, and $1,400 on day 14. $1,050 is 75% of $1,400, which is the amount of the discount if the ticket had been purchased 14 days in advance, so choice (D) is correct.
21. B Go through your checklist of potential errors. Is there a misplaced modifier here? No. Is there a pronoun problem? No. Is there a parallel construction problem? Yes! At first it seems as if this sentence contains a list of three actions: to affect … create … and deteriorate—but wait! The third action is not an action, it’s a noun: deterioration. However, since deterioration is not underlined, we can’t fix this. Going back to the original sentence, it becomes clear that, in fact, there are only two main actions: to affect the overall size of the grapes and (to) create unwanted moisture. To correctly use this compound verb, the original sentence would need an “and” between the verbs. Only choice B gives you this option. Choices C, D, and E use the idiomatic expression “enough that” which is not necessarily wrong, but which would require the word “creating.”
22. C This is a causal argument. The scientists claim that the bat’s near extinction was caused by logging. How do we weaken this argument? By presenting an alternate cause—another reason why the bat almost became extinct. Choices A and B actually strengthen the argument. Choice A says that other species were also threatened with extinction by logging, and choice B gives us a reason the government might have been tempted to agree to logging on federal lands. Choice D is outside the scope of the argument since “sightings” are irrelevant. Choice E also goes outside the scope of the argument by telling us about the bat population on another continent. But choice C gives us an alternate cause for the near extinction of these bats: the sap they depended on for nourishment was severely reduced at the time in question by a five-year drought.
23. E This is a misplaced modifier question. Who was “upset by the recent downturn”? It was the board of directors. This eliminates choices A, B, and C. Choice E correctly positions the prepositional phrase “at its quarterly meeting” and avoids the passive phrase “being added” in D.
24. B This is a statistical argument. The officials assert that there is in fact no increase in actual mishaps during the months after an accident, but an increase in the number of news sources reporting the mishaps—in other words, they argue that the statistics are not representative. To weaken this assertion, we would have to show that the statistics are in fact representative. B does this by implying that certain months are more likely to have more frequent accidents due to high volume of flights. A is outside the scope of the argument. C, D, and E would all strengthen the assertions of the officials.
25. B Most reading comprehension passages ask some form of this question characterized by the phrase “primary purpose.” Choice B best summarizes the main idea of the passage: that despite some potential problems, strategic planning can allow a company to expand and grow.
26. C According to the passage, the difficulty in implementation of strategic plans is a more modern phenomenon, not related to the weaknesses of the 1980s.
27. D Skim the passage quickly to find the survey, then read that portion carefully. According to the passage, the survey shows that companies with strategic plans outperformed companies without strategic plans.
28. D It’s always a good idea to read a few lines above and below the cited lines, just to make sure you understand the context. The financial analysts mentioned in the passage seem to say that it is not worth trying to plan when the market is changing so rapidly. The author mentions their views in order to refute them.
29. C After running down your checklist of potential errors without encountering an ambiguous pronoun, a misplaced modifier, a tense problem, or a subject-verb disagreement, you should begin thinking about the possibility of an idiomatic error. Try making your own sentence: “I no longer deduct … nothing on my taxes.” Does that seem right? In fact, it is incorrect: a double negative.
Scanning the answer choices can give you a clue as well: You have a choice of “nothing” or “anything.” Which is better? If you said “anything,” you were absolutely correct. Choice D includes “anything” but begins with the conjunction “and.”
30. D To get an inference question correct, just look for an answer that you know to be true. Choice A implies that the State Department’s views are always likely to diverge from other news sources, which is an extreme answer, and extreme answers are almost always incorrect. B implies that the State Department should never be used as a news source, which is also extreme. Choice C is never mentioned; therefore, it is out of scope. E is wrong because the answer is too extreme. Choice D is the credited answer because the argument makes it clear that the “alternative” sources of information would provide the “divergent” opinions mentioned in the first sentence.
31. C Go through your checklist of potential errors. Is there a misplaced modifier here? No. Is there a pronoun problem? There certainly is a pronoun here, so be sure to check it out. Is it possible that the “they” could be ambiguous? As a matter of fact, “they” is obviously supposed to refer to the automatic teller machines, but it also could refer to the bank officials. Replacing “they” with “the machines” clarifies the sentence, which means we are down to C, D, or E, but C is correct because D and E are not parallel.
32. E This is a subject-verb question. The verb is in the underlined portion seems to agree with the subject of the sentence, Sweden, but in fact, the noun is must agree with nations, which is plural. We’re down to C, D, or E. C keeps the singular pronoun its, so we can eliminate that. Choice D contains the unidiomatic accepting of, making E the credited answer.
33. A In this causal argument, the decrease in the number of acres of woodland per tiger is said to cause the increasing number of tiger attacks on humans. To strengthen this argument, it would help if the Bengal tigers in areas with a normal number of acres of woodland per tiger have NOT increased their attacks on humans. That’s what A tells us. B gives us an alternate cause for the increase in tiger attacks—in other words, it weakens the argument instead of strengthening it. Choice C adds details without really strengthening the argument. Choice D weakens the scientists’ hypothesis by presenting a possible alternate cause for the tigers’ attacks on humans. Choice E emphasizes the seriousness of the problem without shedding light on its cause.
34. D The tip-off here is the pronoun it. To what does it refer? Not the union nor the management. Really what it seems to refer to is the inability of the two sides to communicate. We can eliminate A and B for that reason. C seems to indicate that it was effective communication that led to the strike. E is both awkward and unidiomatic. Choice D is the correct response.
35. E We are looking for an answer that does NOT weaken the argument. You might think that means the correct answer would strengthen the argument, but while that COULD be the case, it doesn’t have to be. The correct answer might simply be irrelevant to the argument. In this causal argument, more fresh vegetable sales in City X are said to mean that City X has better nutritional habits than City Y. Each of the answer choices pokes holes in that argument, except for E. It suggests that if vegetables are cheaper in City Y, and yet more vegetables are being sold in City X, then the argument that X has better nutritional habits might be right.
36. A In both B and C, the conjunction and wrongly gives the impression that the second half of the sentence is merely an added thought, instead of a new and dangerous development that goes beyond what generally happens. D needlessly changes the verb tense. E’s in a trace amount does not agree with the plural heavy metals.
37. A Choice A best summarizes the main idea of the first paragraph. While D reflects a part of the passage, it does not encompass the main idea of the passage.
38. A The first paragraph gives us the information to answer this question. Note the trigger word however that underscores the difference between the Roman era and the Middle Ages.
39. B The best answer can be found in the first line of the second paragraph. Ransom was one of the few ways a ruler could give his subjects what they wanted to get them to do something he wanted.
40. A To get the answer, we have to understand the meaning of the quoted words, but it also helps to read the rest of the paragraph. The paragraph describes a ransom value that was neither too low nor too high, therefore making A the best answer choice.