单选题 Now that you've gotten a little more confident, we're going to give you the opportunity to practice "without the training wheels." When you want to check your work, you can turn to the solutions at the end. If you aren't familiar with some of the mathematical concepts, make a note to pay particular attention to that chapter in this book; this practice set covers a wide range of topics tested on the GMAT.
On all data sufficiency problems, the answer choices are the same (as you've learned). We've put them here for your reference.
Ａ. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Ｂ. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Ｃ. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
Ｄ. EACH statement ALONE is sufficient.
Ｅ. Statements (1) and (2) TOGETHER are NOT sufficient.

单选题 Is x an integer? (1) x is evenly divisible by

【正确答案】 B

【答案解析】A reminder: The question stem starts with is, so this is a yes or no problem. The first step is to determine whether statement (1) is sufficient, which we can do by trying out some real numbers. If x is 2, which is evenly divisible by [*], then the answer would be yes. But if x were 1.5, which is also evenly divisible by [*], then the answer would be no. Since you can get either yes or no, statement (1) is not sufficient and you should cross off A and D. Now let's move on to statement (2). There are no non-integer numbers that are divisible by 2, so yes is the only possibility. Statement (2) is sufficient, so we can eliminate C and E, and the correct answer is B.

单选题 What is the ratio of 2a to b? (1)

【正确答案】 A

【答案解析】Statement (1) says that [*] We are looking for the ratio [*]. If you substitute 2 for [*] in that ratio, you get 2 times 2, which equals 4. Statement (1) is sufficient. Cross off B, C, and E. How about statement (2)? Remember, you have to forget about the information you got from statement (1). Since there are several values for a and b that would add up to 5, let's try a couple of variations to see if we always get the same ratio. If a is 3 and b is 2, the ratio of 2a to b would be 6:2 or 3:1. But if we used a=2 and b=3 instead (and nothing tells us that we can't), the answer to the question stem becomes 4:3. When we can get different answers, we can tell the statement is not sufficient, so we can eliminate D. A is the correct answer.

单选题 What is the average of a list of n consecutive integers? (1) The smallest number in the list is 5. (2) n=8

【正确答案】 C

【答案解析】Statement (1) tells us the smallest number, but not how many numbers are in the list. It is not sufficient. Cross off A and D.
Statement (2) tells us the value of n, so the question becomes: What is the average of a list of 8 consecutive integers? Since those integers can be large, small, or even negative, we have no way to tell what the average is. Statement (2) is not sufficient, so we can eliminate B.
Now let's put the two statements together. If we know that 5 is the smallest number in a list of 8 consecutive numbers, then we can easily reconstruct the list and find the average. So the statements are sufficient when put together, and the answer is C.

单选题 Is s=r?
(1) s²=r²
(2) s is positive.

【正确答案】

【答案解析】Here's another question that is looking for a yes or no answer. Statement (1) allows for both positive and negative values of both s and r, so we cannot tell ff s = r. Statement (1) is not sufficient; cross off A and D. Statement (2) just tells us that s is a positive number; we don't know anything about r at all and cannot tell if they are equal; statement (2) alone is not sufficient. Let's eliminate B. What if we combine the two? Statement (2) tells us that s is positive, but r could still be either positive or negative. We still cannot tell if they are equal, so the answer is E.

单选题 In triangle ABC, what is the length of AB? (1) The length of BC is 5 and the length of AC is 12. (2) Angle C=90°.

【正确答案】 C

【答案解析】Statement (1) alone is tempting if you are familiar with the right triangles that tend to be tested over and over on the GMAT; however, we don't know from statement (1) that ABC is a right triangle, so we should cross off A and D. With only statement (2), we certainly don't have enough information to answer the question, so B can be eliminated. Together, though, we can complete the picture of a right triangle with two known sides, which means we can figure out the third side using Pythagorean Theorem, and our answer is C. (Since the squares of the two legs add up to 169, the hypotenuse is 13.)

单选题 If there are only red, blue, and green marbles in a jar, what is the ratio of red to blue marbles? (1) The ratio of red to green marbles is 2:3. (2) The ratio of green to blue marbles is 6:5.

【正确答案】 C

【答案解析】Statement (1) doesn't give us any information about the number of blue marbles at all. It is not sufficient and we can cross off A and D. Statement (2) doesn't give us any information about the number of red marbles, so we can eliminate B. When we combine both statements, we have ratios that involve all three colors of marbles. Let's see what happens when we use some real numbers. If there are 6 green marbles, then there are 4 red marbles and 5 blue marbles, making the ratio of red to blue marbles 4:5. If we used a different number for the green marbles--say, 12--we would end up with the same ratio of red to blue. This happens frequently with relative numbers such as ratios, proportions, averages, and probability; keep in mind that you don't always have to know the actual numbers to know the ratios. Statements (1) and (2) together are sufficient, so the answer is C.

单选题 Over a holiday weekend, a certain car dealer sold off 4 of the cars on its lot. If the cars sold for an average of $6,000 each, how many cars were on the dealer's lot at the beginning of the weekend? (1) The average value of the remaining cars on the lot is $5,000. (2) The car dealer made $48,000 in car sales over the weekend.

【正确答案】 B

【答案解析】Given statement (1) alone, we only know average values of both the cars that were sold and the cars that remained; the dealer could have sold 4 cars and had 1 left, or sold 8 cars and had 2 left, or an infinite number of other options. So we can eliminate A and D. With statement (2), we are able to find the number of cars sold by dividing the total sales by the average price. 48,000/6,000=8, so the dealer sold 8 cars. Since that is [*] of the cars on the lot, the dealer started off with 10 cars. Statement (2) is sufficient, so the answer is B.

单选题 What is the value of

? (1)

【正确答案】

【答案解析】Statement (1) doesn't tell us about g at all, so it is insufficient, and we can cross off A and D. Similarly, statement (2) doesn't tell us about f, so we can eliminate B. If we put the statements together, we have only two equations for our three variables, so we still cannot solve. Since the statements together are not sufficient, the answer is E.

单选题 Was the price of a certain stereo in March greater than its price in May? (1) The price of the stereo in March was 80 percent of its price in April. (2) The price of the stereo in April was 120 percent of its price in May.

【正确答案】 C

【答案解析】Again, this problem is looking for a yes or no answer. Statement (1) doesn't tell us anything about the May price, so it is not sufficient. We can cross off A and D. Statement (2) doesn't tell us anything about March, so it is not sufficient and we can cross off B. With both statements together, we know relative prices, and no matter what numbers we were to assume, the May price ends up slightly higher than the March price. So the answer is definitely no, meaning that both statements together are sufficient, and the answer is C.

单选题 If the square root of t is a real number, is the square root of t positive?
(1) t＞0
(2) t²＞0

【正确答案】

【答案解析】This question is looking for a definite yes or no answer. Statement (1) is not sufficient since all it tells us is that t is a positive number. Unless the radical sign ([*]) is used, a positive number has two square roots, a positive root and a negative root. For example, if t is 4, then it has two square roots, 2 and -2. So we can eliminate A and D. With statement (2) alone, we don't get much more information; all it really tells us is that t is a positive number (it cannot be negative, since the square root of a negative number is a complex number, not a real number). So again, t could be 4, and its root could be either positive or negative. So we can eliminate B. Putting them both together doesn't tell us whether the square root of t is positive either, so our answer has to be E.

单选题 If the ratio of brown cars to blue cars in a certain parking lot is 2:3, how many brown cars are in the lot? (1) There are 15 blue cars in the lot. (2) There are 25 cars total in the lot.

【正确答案】 D

【答案解析】When we evaluate statement (1), we can tell that there are 10 brown cars in the lot, because that's the only number that would give us a ratio of 2:3 if there are 15 blue cars. So we can eliminate B, C, and E. Taking statement (2) alone, we can tell that we have 15 blue and 10 brown cars in the lot, because those are the only numbers that would add up to 25 and give a ratio of 2:3. So either statement is sufficient on its own, which means D is the correct answer.

单选题 What is the value of f²-g²?
(1) f=-g+8
(2) f=g-2

【正确答案】 C

【答案解析】When we see a quadratic formula like f²-g², we almost always want to simplify it to see its parts better. This formula simplifies into (f+g)(f-g), so if we can get values for each of those parenthetical statements, we can calculate the value of the whole. Statement (1) gives the value of f+g when it is rearranged, but doesn't give the value of f-g. We can cross off A and D. Statement (2) gives the opposite: the value of f-g only. So it is not sufficient on its own--we can cross off B--but the two statements are sufficient together, so C is the correct answer.

单选题 A shelf contains only books of poetry, short stories, and non-fiction. If Jana draws a book randomly off the shelf, what is the probability that the book will be non-fiction? (1) There are 15 books on the shelf. (2) There are 4 books of poetry and 5 books of short stories on the shelf.

【正确答案】 C

【答案解析】Statement (1) doesn't tell us anything about the breakdown of the different types of books, so we don't know how likely Jana is to draw a non-fiction book. Eliminate A and D. Statement (2) alone doesn't tell us anything about the number of non-fiction books. So we can eliminate B. Putting the statements together, we can tell that there are 6 non-fiction books on the shelf by subtracting 4 and 5 from 15. Therefore, Jana has a [*] probability drawing a of non-fiction book at random, and our answer is C.

单选题 A job opening was posted in September and again in January. In September, the number of applicants for the position was 60. What was the percent change in the number of applicants from September to January? (1) The number of applicants in January was one-third the number of applicants in September. (2) The number of applicants in January was 20.

【正确答案】 D

【答案解析】Statement (1) lets us find the number of January applicants (20) and then we can find that the percent change in applicants was 66 3 %, so it is sufficient and we can eliminate B, C, and E. Statement (2) tells us the same thing; it is also sufficient, so we can cross off A and we are left with D.

单选题 Is a³＞20?
(1) a⁴＞80
(2) a⁵＞200

【正确答案】 B

【答案解析】Here's another question that is looking for a yes or no answer. Statement (1) allows for both positive and negative values of a, so it is not sufficient, and we can cross off A and D. Statement (2), on the other hand, tells us that a is positive and must be a value of at least 3. If a＞3, then the answer to the question stem must always be yes. Therefore, statement (2) is sufficient, and our answer is B.

单选题 What is the length of a side of a certain cube? (1) The volume of the cube is 27. (2) The surface area of the cube is 54.

【正确答案】 D

【答案解析】Statement (1) tells us that the length of a side of the cube is 3, since the volume is just the length of one side cubed. So we can cross off B, C, and E. Statement (2) is a little trickier, since surface area is generally a less familiar concept. If the surface area of the whole cube is 54, then the area of each one of the 6 faces is 9. That means each side is 3, so statement (2) is also sufficient, and our answer is D.

单选题 How many prime factors of x are also prime factors of y? (1) x=30 (2) y is a multiple of x.

【正确答案】 C

【答案解析】Statement (1) tells us nothing about the prime factors of y, so it is not sufficient on its own. We can eliminate A and D. We do know at this point, though, that the set of prime factors in question is {2, 3, 5}. Statement (2) on its own tells us nothing about the prime factors of x, so it is not sufficient on its own. We can eliminate B. Putting them together, we can see that all of the prime factors of x would also be prime factors of y, so they have those same three prime factors in common. Since the statements are sufficient together, then answer is C.

单选题 Is m＞0?
(1)

【正确答案】 B

【答案解析】Statement (1) is not sufficient because m could equal either 4 or -4, giving us either a yes or a no. So we can eliminate A and D. Statement (2) tells us that m has to be positive 4, so it is sufficient, and our answer is B.

单选题 What is the value of

? (1)

【正确答案】 A

【答案解析】Statement (1) tells us the value of the reciprocal of [*]. That means [*]has to equal [*], so statement (1) is sufficient and we can eliminate B, C, and E. Statement (2) alone tells us nothing about w and very little about V, so it is not sufficient. A is our answer.

单选题 There are twenty students in a class, all of whom scored between 0 and 100 on their final exams. If the class average was 85, how many people scored below the average score on the exam? (1) Twelve people in the class scored higher than an 85. (2) The lowest eight scores added up to 640.

【正确答案】

【答案解析】Statement (1) is tricky because it implies that eight people scored lower than 85, but in fact, it is possible according to the question for some people to have scored exactly an 85, so it is not sufficient and we can eliminate A and D. Statement (2) doesn't really give us any information; it tells us that the lowest eight scores had an average of 80, but we don't know how many of those scores were below 85. So we can eliminate B. Putting the statements together, we can tell that 12 people made above an 85 and the 8 others had an average of 80, but we can't tell how many of the 8 were below an 85, so we have to eliminate C. E is our answer.

单选题 Advertisement:
Of the many over-the-counter medications marketed for the relief of sinus headache, SineEase costs the least per dose. And SineEase is as effective per dose as the most effective of those other medications. So for relief from sinus headaches, SineEase is the best buy.
Which of the following, if true, most seriously weakens the argument above?

A. Most of the over-the-counter medications marketed for the relief of sinus headache are equally effective per dose in providing such relief.
B. Many of the over-the-counter medications marketed for the relief of sinus headache contain the same active ingredient as SineEase.
C. People who suffer from frequent sinus headaches are strongly advised to consult a doctor before taking any over-the-counter medication.
D. An over-the-counter medication that is marketed for the relief of symptoms of head cold is identical in composition to SineEase but costs less per dose.
E. The per dose price for any given over-the-counter medication marketed for the relief of sinus headache is higher for smaller packages than it is for larger packages.

【正确答案】 D

【答案解析】[解析] 本题难度较大。其逻辑推理为：缓解窦头痛的非处方药中，SineEase成本低，所以缓解窦头痛最好用SineEase。简化推理就变为“因为SineEase成本低，所以购买SineEase”，(A)中的“equally”与(B)中的“the same... as”揭示的是相同点，不可能Weaken上面推断；(C)中any绝对化语言必然不对；(E)为无关比较；而(D)说明某药组成与SineEase一样，但每剂成本更低，起到了反对作用。很多同学之所以不理解(D)为什么正确，主要是忽略了(D)中的“identical in composition”。试想若某药与SineEase组成完全一样，那么它必可被用来缓解窦头痛且达到同样的效果，但它成本更低，因此更好地选择应为这种药，值得注意的是(D)并未反对事实，段落中的事实是SineEase是缓解窦头痛的非处方药中最便宜的，而(D)中的某种药是缓解感冒症状的非处方药中最便宜的。

单选题 Crimes are mainly committed by the young, and for this reason merely increasing the number of police officers or expenditures on police services has little effect on reducing the crime rate. In fact, the only factor associated with a crimerate drop is a decrease in the number of People in the community aged fourteen to thirty.
The findings above can best serve as part of an argument against

A. the likelihood that any law enforcement program will be effective in reducing the crime rate within a short time.
B. increasing prison terms for young people found guilty of crimes.
C. introducing compulsory military conscription for people aged seventeen to nineteen.
D. raising the age at which students are permitted to leave school.
E. a community's plan to increase the number of recreational and educational activities in which young adults can participate.

【正确答案】 A

【答案解析】[解析] 本题问题目的是上述发现能够驳斥下面哪一个，一般是把段落中的main idea取非即为答案。上面段落里的“the only factor...”取非，即(A)表明任何方案都可能只在短期内有效，所以与上面推理相违背，因此(A)正确；(E)易误选，选(E)的人认为娱乐、教育增加可以减少犯罪，从而反对了上面的“the only factor...”，但这是递推出来的，实际上(E)与犯罪率减少一点关系也没有，因此(E)不正确。

单选题 A member of the British Parliament is reputed to have said, "The First purpose of good social reform is to increase the sum total of human happiness. So, any reform which makes somebody happy is achieving its purpose. Since the reform I propose would make my constituents happy, it is a good social reform. "
Which one of the following, if true, most seriously weakens the argument attributed to the member of Parliament?

A. Different things make different people happy.
B. The proposed reform would make a few people happy, but would not increase the happiness of most other people.
C. The proposed reform would affect only the member of Parliament's constituents and would make them happy.
D. Increasing some people's happiness might not increase the sum total of human happiness if others are made unhappy.
E. Good social reforms usually have widespread support.

【正确答案】 D

【答案解析】[解析] 这个议员的论述只是说明他提出的改革使部分人幸福，而没有证明他提出的改革不会给其他人带来不幸。因此(D)是最佳选项。