Executive Assessment Mock Test - 5 - GMAT MCQ

The regression line comes close to the points (0,12) and (5,5). Therefore, the approximate slope is

After 0 days of training, only two students were able to get within 11 in. of the target. After two days of training, there were four students who were able to get with 11 in. of the target. There was definitely an increase, so eliminate A and B. Now, to get the percent increase, you need to do

The regression line is decreasing. Therefore, as the number of days increase, the distance a student is able to get from the target decreases. This is a negative relationship.

Most Strengthens: Choice C

Once a geo-engineering innovation has been passed by the committee, the same innovation is automatically approved in all subsequent projects, without further review.

In disagreeing with the XM representative, the federal committee member has based her rebuttal on the statement that if we fail to review your project, we also fail to observe innovations in geo-engineering that may need guidelines drafted for the safety of subsequent projects throughout the industry. Setting a precedent for future projects is therefore the central concern of the committee member. To strengthen her argument, you need additional evidence that supports this assertion. Answer (C) states that once an innovation has been passed, the same innovation in subsequent projects is passed without further review. Including this additional evidence undermines the XM representative’s claim that the project should be passed without review and thus supports the committee member’s rebuttal.

Most Weakens: Choice A

XM’s latest project is nearly identical to a previous project by XM that had successfully passed the committee review process.

The XM representative claims that the costly and time-consuming review should be waived so that our latest project can be quickly passed and implemented. The federal committee member disagrees because doing what the representative suggests could mean the committee would also fail to observe innovations in geo-engineering that may need guidelines drafted for the safety of subsequent projects throughout the industry. To weaken the committee member’s argument, you need evidence that suggests that no such failure to observe innovations will occur in this case. If XM’s latest project is identical to a previous project by XM that had successfully passed the committee review process, as answer choice (A) states, then there are no innovations to consider. This weakens the federal committee member’s argument, and provides additional support for the XM representative’s request.

Insect Species X: Choice A, 450

Insect Species Y: Choice C, 565

First, note that, if the populations are to become equal in four years, at a 10% and a 15% rate of decrease, respectively, then the two populations are not currently equal. Additionally, the current population of Insect Species Y must be more than the current population of Insect Species X, in order for their totals to converge, at these independent rates of decrease, in four years. Therefore, the current population of Insect Species X cannot be 625, and the current population of Insect Species Y cannot be 450.

The problem requires working with two unknowns: the current population of Insect Species X and the current population of Insect Species Y. Therefore, Plug In The Answers to determine which will satisfy the conditions of the question. To approach the problem most efficiently, recognize that a 10% decrease is the same as taking 90% of the original number. Suppose that the current population of Insect Species X is 500. A 10% decrease from 450 is equivalent to 90% of 500, or (.9)(450), which is 405. That would be the decrease for one year. To find the decrease for the next year, you would need to begin with the adjusted population and decrease from there: a 10% decrease from 405 is equivalent to (.9)(405), which is 364.5. So, finding the decrease for two subsequent years from a current population of 450 is equivalent to calculating (.9)(.9)(450) = 364.5. Similarly, finding the decrease for four subsequent years at a 10% rate from a current population of 450 is equivalent to calculating (.9)(.9)(.9)(.9)(450) = (.6561)(450) = 295.245. So, to find the decreased population of Insect Species X for four years at a 10% rate, you would calculate (.6561)(current population X).

A 15% decrease is the same as taking 85% of the original number, so to find the decreased population of Insect Species Y for four years at a 15% rate, you would calculate (.85)(.85)(.85)(.85)(current population Y), or approximately (.522)(current population Y).

To determine what two current populations will be equal (rounded to the nearest million) in four years, you are looking for values that satisfy the equation (0.6561)(current population X) = (0.522)(current population Y). Now you can simply calculate with each value provided to see what the future populations would be:

Rounded to the nearest million, the values that satisfy the equation (0.6561) (current population X) = (0.522)(current population Y) are 450 for the current population of Insect Species X and 565 for the current population of Insect Species Y, which would both decrease to approximately 295 million, at their independent rates of decrease, in four years.

Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual.

Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.

Statement 1:  Amudha, Bharatan, and Chandran are mutual strangers.

⇒ A and B are strangers. A and C are strangers. B and C are strangers.

Statement 2:  Amudha, Dhinesh, and Fani are Ezil's friends.

⇒ A and E are friends. D and E are friends. F and E are friends. 

Statement 3: Chandran and Gowtham are friends.

⇒ C and G are friends.

Now, it is give that every person is either friend, acquaintance or stranger to the other six. Thus, Sum of the number in each row should be 6.   

⇒ No of Friends of A = 6 - 4 - 1 = 1 

⇒ No of friends of G = 6 - 3 - 2 = 1

Statement 4: Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.

therefore, Amudha's only friend Ezhil will be the only acquaintance of Bhutan.

Similarly,

Statement 5: Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

therefore, Amudha's only acquaintance will be Bhutan's friend.

⇒ Bhutan's number of friends and acquaintance is 1 each, thus, number of strangers become 6-1-1 = 4.

Now, we can conclude that Bhutan's friend will be Dhinesh. ⇒ Amudha's acquaintance will be Dhinesh.

Reason: Bhutan can't be friends with acquaintances and strangers i.e. Ezhil, Amudha, and  Chandran. Moreover, Fani's only friend is Ezhil and Gowtham's only friend is Chandran. thus, only Dhinesh is left as an option.

Now, since Dhinesh is an acquaintance to Amudha, Fani and Gowtham will be strangers to Amudha.

Similarly, since Dhinesh is a friend of Bhutan, Fani and Gowtham will be strangers to Bhutan.

Now, Gowtham has 1 friend (Chandan) and 2 strangers (Amudha, Bhutan), thus, 3 Acquaintances will be Dhinesh, Ezhil and Fani.

further, we can conclude that (B,E) are Dhinesh's friend and (A,G) are Dhinesh's acquaintance. thus, Dinesh has 2 friends, acquaintances and strangers each. moroever, Strangers to Dhinesh will be (C,F).

Since, Gowtham and Ezhil are acquaintances. we can conclude that Ezhil has 3 friends (A,D,F) , 2 acquaintances (B,G) and 1 Stranger (C).

For Chandran, from the table we can conclude that he has 1 friend, 1 acquaintance and 4 strangers. where, Fina will be the acquaintance.

Thus, Fina will have 1 friend, 2 acquaintance and 3 strangers.

FINAL TABLE:

(Bharatan, Ezhil) and (Fani, Gowtham) ⇒ acquaintances and acquaintances (SIMILAR)

Amudha, Bharatan, Chandran, Dhinesh, Ezhil, Fani and Gowtham are seven people in a town. Any pair of them could either be strangers, acquaintances, or friends. All relationships are mutual.

Partial information about the number of friends, acquaintances, and strangers of each of these people among them is given in the table below.

Statement 1:  Amudha, Bharatan, and Chandran are mutual strangers.

⇒ A and B are strangers. A and C are strangers. B and C are strangers.

Statement 2:  Amudha, Dhinesh, and Fani are Ezil's friends.

⇒ A and E are friends. D and E are friends. F and E are friends. 

Statement 3: Chandran and Gowtham are friends.

⇒ C and G are friends.

Now, it is give that every person is either friend, acquaintance or stranger to the other six. Thus, Sum of the number in each row should be 6.   

⇒ No of Friends of A = 6 - 4 - 1 = 1 

⇒ No of friends of G = 6 - 3 - 2 = 1

Statement 4: Every friend of Amudha is an acquaintance of Bharatan, and every acquaintance of Bharatan is a friend of Amudha.

therefore, Amudha's only friend Ezhil will be the only acquaintance of Bhutan.

Similarly,

Statement 5: Every friend of Bharatan is an acquaintance of Amudha, and every acquaintance of Amudha is a friend of Bharatan.

therefore, Amudha's only acquaintance will be Bhutan's friend.

⇒ Bhutan's number of friends and acquaintance is 1 each, thus, number of strangers become 6-1-1 = 4.

Now, we can conclude that Bhutan's friend will be Dhinesh. ⇒ Amudha's acquaintance will be Dhinesh.

Reason: Bhutan can't be friends with acquaintances and strangers i.e. Ezhil, Amudha, and  Chandran. Moreover, Fani's only friend is Ezhil and Gowtham's only friend is Chandran. thus, only Dhinesh is left as an option.

Now, since Dhinesh is an acquaintance to Amudha, Fani and Gowtham will be strangers to Amudha.

Similarly, since Dhinesh is a friend of Bhutan, Fani and Gowtham will be strangers to Bhutan.

Now, Gowtham has 1 friend (Chandan) and 2 strangers (Amudha, Bhutan), thus, 3 Acquaintances will be Dhinesh, Ezhil and Fani.

further, we can conclude that (B,E) are Dhinesh's friend and (A,G) are Dhinesh's acquaintance. thus, Dinesh has 2 friends, acquaintances and strangers each. moroever, Strangers to Dhinesh will be (C,F).

Since, Gowtham and Ezhil are acquaintances. we can conclude that Ezhil has 3 friends (A,D,F) , 2 acquaintances (B,G) and 1 Stranger (C).

For Chandran, from the table we can conclude that he has 1 friend, 1 acquaintance and 4 strangers. where, Fina will be the acquaintance.

Thus, Fina will have 1 friend, 2 acquaintance and 3 strangers.

FINAL TABLE:

ACQUAINTANCE OF AMUDHA = DHINESH

The question wants you to find out whether in the Q4, the ratio of sales to inventory for HR~tubes is more than that for other products.

Mathematically, this means that for Q4,

⇒ 

You have nine products for which you need to calculate the sales-to-inventory ratio, but that would be too time-consuming, and hence it is not advisable to compute.
A better approach would be to calculate a few select values. You know that for HR tubes, the value is 4.5, which is more than 1. You can skip the products for which sales are less than their inventory as the sales-to-inventory ratio value would be less than 1.
Secondly, you can mentally divide sales by inventory to get probable contenders that have values, equalling more than 4. There is only one such product: HR sheets, which has a sales-to-inventory value equal to 14/3 = 4.6714/3 = 4.67, more than 4.5, so the statement is wrong.

The answer for part B is "No."

The question wants you to find out whether median sales for Q1 is more than median sales for each of Q2, Q3, and Q4.

Mathematically, this means:

To get the median sales of each quarter, sort the table by its sales columns to get the table:

Median Sales for Q1:

Median of a series = value of the  term

Here, median sales for Q1 equals:

Value of  product = value of the 5.5^th product.

The value of the 5.5th product equals

Average of 16 & 18 = (16+18)/2 = 17 MT
Similarly, median sales for Q2, Q3, and Q3 are (15 + 15)/2 = 15, (8 + 15)/2 = 11.5, and (13 + 13)/2 = 13 MT, respectively. Hence, the statement is correct.

The answer for the part C is "Yes."

1. The complex and somewhat ambiguous issue of the legality of SWIFT's cooperation can be inferred by the fact that legal reasons exist both for cooperating and for not cooperating. For cooperating: "it could be argued that the program was legal because the United States government possesses the authority to subpoena records stored within its territory and SWIFT maintained many of its records in Virginia" For not cooperating: "international law must be upheld and one could argue quite strongly that the government's use of data breached some parts of international law"
2. The passage enables us to infer the contrary by implying that SWIFT considered the legal implications of not cooperating ("SWIFT executives undoubtedly considered the aforementioned reasons [one being legal] for rejecting the government's subpoena").
3. The passage never discusses the volume of money (only the number of transactions). Moreover, there is no comparison of money or transactions before and after SWIFT's decision became public.
4. There is no information in the passage that allows anything close to this inference. The passage never mentions threats or government efforts to force SWIFT to comply.
5. Although this did in fact occur, there is no information in the passage that allows anything close to this inference.

The important quote from the passage is: "cooperating with the government did not explicitly violate any SWIFT policies due to the presence of a valid subpoena"

1. An ethical argument for SWIFT complying is that the data are located in Virginia. This does not mean (and it would be wildly improper to conclude) that all the data pertains to U.S. citizens. The article implies that SWIFT deals with the financial information of people in the international community. Further, the article does not explicitly say that the U.S. government wanted information about its citizens.
2. The passage states that we cannot answer the following question: "what, if any, potentially impending threats did the government present to justify its need for data?" Given the inability to answer this, there are no grounds to conclude that SWIFT executives believed another attack was imminent.
3. This answer closely restates the third reason given for complying. Since the article makes clear that the government presented a valid subpoena, the data the government sought resided in the U.S., and complying with such subpoenas did not violate SWIFT policy, this answer is correct.
4. The passage states the opposite, noting that one unanswered question was: "What promises did the government make about data confidentially?"
5. The passage never mentions that SWIFT received information about why data were being subpoenaed. In fact, we can infer that SWIFT likely did not based upon the fact that one remaining unanswered question was: "What, if any, potentially impending threats did the government present to justify its need for data?"

The fundamental flaw in the argument is that it is comparing unlike parts. Specifically, the argument is comparing the net value of assets held by or in the name of a group with the net value of assets held by (and not in the name of) another group. It is quite possible that the large value of assets held for children or beneficiaries (e.g., trusts and estates) comprise large amounts of money.

1. The argument notes that the study considered "the net value of assets" (i.e., assets minus liabilities). Consequently, the study did adequately account for the role of debt in acquiring assets.
2. Eliminating one's debt via bankruptcy would not be unique to the twenty something demographic nor would debt spending change the value of net assets held in one's name.
3. The information about the tax code does not undermine the conclusion of the study. Instead, it simply provides an explanation for why the value of assets (not necessarily net assets) is larger than expected among twenty somethings (i.e., tax incentives fueled it).
4. The argument is not based upon the exact amount of spending between age groups. Rather, the argument is based upon relative spending and saving between age groups.
5. The argument compares the assets held by and for the benefit of someone with the assets held by (and not for) a different type of person. This unlike comparison is not sufficient logical grounds to make an argument comparing the two groups.

The conclusion to the argument is that "Samuel is obviously a bad fisherman" while the premise is Samuel's poor fishing performance relative to the peers on his fishing boat this past season.

The argument is flawed as the conclusion does not follow from the premise. The line of reasoning fails to take into consideration other possibilities for Samuel's performance this past season: perhaps Samuel fished with different bait. Similarly, just because Samuel caught fewer fish in one season than five other individuals does not mean that he is a bad fisherman. It simply means that he caught fewer fish than five individuals in one season. This season could have been an exception in Samuel's career or his teammates could be far above average.

A. The same logical flaws are at play in this answer (except in reverse). Using one season and a comparison to the fishermen on one boat does not provide a wide enough basis to make a judgment about a fishermen's ability relative to all other fishermen. Comparing this past season with another season still does not help to explain Samuel's poor performance this season (whereas knowing that Samuel used experimental bait this season would provide a justification for why Samuel caught few fish yet was still not a terrible fisherman).
B. Samuel's performance as a pilot does not relate to his ability as a fisherman. This answer is off topic.
C. On first glance, this looks like a good answer. However, it does not consider whether Samuel's teammates were sick during the same period. Perhaps one of Samuel's teammates was sick for two weeks.
D. This answer highlights something that made Samuel's fishing performance uniquely different than his teammates. Moreover, Samuel did not make the choice to fish with alternative bait--his captain ordered him to do it. If Samuel made the choice to fish with alternative bait, it would be his poor fishing judgment that would be at fault. Similarly, the answer makes clear that no other fisherman on Samuel's boat faced the same predicament.
E. If anything, this answer strengthens the argument.

The conclusion to the argument is that "when the industry completes its transition to the new cork, there will no longer be any threat to landfills from red wine corks." The conclusion omits an important fact: even after manufacturers stop making the old wine corks, there will still be thousands of old bottles in circulation. Individuals who purchased red wine bottles years ago will consume them and discard the old corks in landfills, thereby continuing to pollute landfills. Consequently, we cannot conclude that "there will no longer be any threat to landfills from red wine corks."

To further see that this is the conclusion, consider the points of the argument and which points support a conclusion versus which point is a conclusion supported by other points. The points of the argument are:
(1) red wine corks pose a threat to the environment
(2) a solution has been found
(3) when the industry adopts the solution, the threat will be gone

Notice that it makes no sense to say that since (3) is true, therefore (1) must be true, as would be the case if (3) were a premise and (1) were a conclusion. Instead, it makes sense to say that since (1) and (2) are true, therefore we conclude (3). Now the task at hand is to see how even though (3) is the conclusion, it is not an extremely sound conclusion.

A.. The timing of the industry's transition is irrelevant due to the qualifier in the conclusion: "when the industry completes its transition to the new cork."
B. This statement properly identifies a weakness in the conclusion.
C. The time taken to produce a cork does not impact matters of pollution.
D. At first glance, this answer has some appeal. However, the conclusion relates to pollution in a landfill--not fumes omitted into the air during production.
E. The cost to produce the new cork is not pertinent in a consideration of landfill pollution.

There are two main problems with the original sentence.

(1) The original sentence contains an improper idiom. The idiom as many x than is not idiomatically correct and should be replaced by the idiomatically correct phrase as many x as.

(2) would be killed in World War I is illogical as it is in the future tense, implying that World War I occurred after World War II. The phrase could be made significantly more concise using as many lives as World War I. The words would be killed in or were killed in are not necessary and should be omitted.

A. The idiom as many ... than is incorrect; the use of the future tense causes the sentence to illogically imply that World War I occurred after World War II
B. The use of the future tense causes the sentence to illogically imply that World War I occurred after World War II
C. The idiom as many ... than is incorrect; those who were killed in is awkward and unnecessary
D.The idiom as many ... than is incorrect
E. The correct idiom is used (as many ... as); the sentence correctly implies that World War II occurred after World War I; the unnecessary phrase were killed in is omitted
 

(1) The sentence must be constructed such that corresponding consequences of an action are parallel. Specifically, the sentence should read enabled political candidates with cash-strapped budgets to x and y where x and y are parallel.

(2) The phrase to be able to z is redundant and should be replaced by to z

(3) The phrase numbers of money should be amounts of money since number is only used when the object in question can be counted and money cannot be counted (i.e., you do not say 1 money, 2 money, 3 money). Note: By comparison, dollars can be counted (i.e., you would say 1 dollar, 2 dollars, 3 dollars) and as a result, we would say: the number of dollars.

A. the phrase to be able to reach is redundant and can be shortened as follows: to reach; large numbers of money is not grammatically correct since money itself cannot be counted and, as a result, amount should be used instead
B. the phrase to reach...and be successful is not parallel
C. this sentence is set up such that succeeding modifies reaching voters instead of being a separate action on its own
D. the phrase is parallel (i.e., to reach...[to] succeed); to be able to reach is replaced by the shorter to reach
E. the phrase to be able to reach is redundant and should be replaced by to reach

A modifying phrase needs to be placed by the word it modifies. However, as the sentence is originally written, after years of working on Wall Street illogically modifies an apartment. It was not the apartment that worked for years on Wall Street but famed investment banker John E. Callan who worked for years on Wall Street. The sentence can be corrected in two ways:
(1) After years of working on Wall Street, famed investment banker John E. Callan
(2) OR: After years of working on Wall Street, John E. Callan

A. an apartment in lower Manhattan is illogically modified by the phrase after years of working on Wall Street
B. famed investment banker John E. Callan is logically modified by the phrase after years of working on Wall Street
C. an apartment in lower Manhattan is illogically modified by the phrase after years of working on Wall Street
D. the phrase he too is not grammatically correct since it implies that there is another person who also owned a house in Rye and in East Hampton; the word too should be removed
E. the phrase even despite his owning of is not idiomatically correct and should be replaced by even though he also owned

There are two major problems with this sentence.

(1) The subject (his writings, which is plural) does not agree with the verb (is, which is singular). Since the words his writings are located outside the underlined portion, the verb is must be changed to are.

(2) The idiom more often than is intended to compare the writings of Douglas Kysar with the writings of other young legal scholars. However, the original sentence compares Kysar's writings with other young legal scholars. It does not make sense to compare writings to people. The correct comparison should compare the writings of Kysar to those of most other young legal scholars, where the pronoun those clearly refers to legal writings--not young professors.

A. The subject (his writings, which is plural) does not agree with the verb (is, which is singular); the writings of Douglas Kysar are illogically compared to other young legal scholars
B. The writings of Douglas Kysar are illogically compared to other young legal scholars
C. The subject (his writings, which is plural) does not agree with the verb (is, which is singular)
D. The subject (his writings, which is plural) correctly agrees with the verb (are, which is plural); the writings of Douglas Kysar are correctly compared to those [referring to writings] of most other young legal scholars
E. The writings of Douglas Kysar are illogically compared to other young legal scholars; the are is awkward

There are two main issues being tested in this sentence.

(1) When using like or unlike, you must compare like parts (e.g., compare arguments with arguments). The original sentence improperly compares the team of lawyers with the government's argument.

(2) The expression , which modifies the term that is immediately before it. For example, the phrase the argument from the petitioner, which rested on a questionable interpretation of a bill that only recently passed Congress is incorrect since it was not the petitioner that rested on a questionable interpretation, but rather the argument that rested on a questionable interpretation.

A. the sentence illogically and improperly compares unlike parts (i.e., it compares the team of lawyers with the government's argument)
B. the phrase the argument from the petitioner, which rested on a questionable interpretation of a bill that only recently passed Congress is incorrect since it was not the petitioner that rested on a questionable interpretation, but rather the argument that rested on a questionable interpretation
C. the sentence properly compares like parts (i.e., it compares the petitioner's argument with the government's argument); , which rested on... properly and logically modifies the phrase it follows
D. the phrase whose case rested on is illogical since whose (which should modify a person) is actually modifying an argument
E. the original sentence, which reads a bill that only recently passed Congress, is perniciously changed to a new sentence, which reads a bill that recently only passed Congress; the difference in meaning between a bill that recently only passed Congress (meaning it did not become law) and a bill that only recently passed Congress (meaning it passed Congress a short time ago) is significant

Since the numerator of aU of the fractions in the answer choices is 0.03, the least of the fractions will, be the fraction with the greatest denominator. The greatest denominator is 7.1, and so the least of the fractions is 0.03/7.1

Arthmetic means = sum of total numbers /numbers
(j + j + 5 + 2j-1 + 4j - 2 + 5j - 1)/5 = 8
(13j + 5 - 4)/5 = 8
(13j + 1) = 40
13j = 40 – 1 = 39
j = 39/13 = 3 ans.

The area of a rectangle can be found by multiplying the length and width of the rectangle. Therefore, the combined area, in square meters, of the 2 rectangular tracts of land is (300)(500) + (250)(630) = 150,000 + 157,500 = 307,500.

We can create the following equations:

A = 2E
B = E + 3
C = 2B
D = B + E
Let’s substitute B = E + 3 in the last two equations:
C = 2(E + 3) = 2E + 6
D = (E + 3) + E = 2E + 3
Now, we have everything expressed in terms of E; thus it just remains to compare the quantities 2E, E + 3, 2E + 6, 2E + 3 and E. Since E is the number of properties sold by Ellen, it is a positive integer. Thus, the greatest expression among the five possibilities is 2E + 6, which belongs to Cary.

Andrew participated in 1 event and scored 9 points, so his overall score was 9/1 + 1 = 10. Jason participated in 3 events and scored 5 + 6 + 7 = 18 points, so his overall score was 18/3 + 3 = 9. The ratio of Andrew’s overall score to Jason’s overall score was 10/9.

The work plan requires that the team produce an average of 200 items per day in September. Because the team has only produced an average of 150 items per day in the first half of September, it has a shortfall of 200 - 150 = 50 items per day for the first half of the month. The team must make up for this shortfall in tire second half of the month, which has an equal number of days as the first half of the month. The team must therefore produce in the second half of the month an average amount per day that is 50 items greater than the required average of 200 items per day for the entire month. This amount for the second half of September is 250 items per day.
The correct answer is B.

Statement 1:

We are given that the combined price of 39 oranges and 36 apples is $111.

Looking at the numbers (13,12) in the question statement and (39,36) in Statement (1), it must click that 39 is 3 times of 13, and 36 is also 3 times of 12. Thus, we have:

The combined price of 39 (= 13 × 3) oranges and 36 ( = 12 × 3) apples is $111.

Thus, the combined price of 13 oranges and 12 apples is $111 / 3. - Sufficient

Note: Since in Data Sufficiency questions, you only have to assess whether a statement can lead you to a unique answer or not, do not waste time in calculating the exact answer. This is why the value $1113 has not been further simplified. There is simply no need to do so.

Statement 2:

We are given that the combined price of 3 oranges and 2 apples is $7.

Getting a cue from dealing with Statement (1), we see that 12 is 6 times of 2, but 13 is not 6 times of 3. So, by multiplying the information "the combined price of 3 oranges and 2 apples is $7" by 6, we cannot reach "the combined price of 13 oranges and 12 apples…"

We would rather get:

6 × (Combined price of 3 oranges and 2 apples is $7)
= Combined price of 18 oranges and 12 apples is $42, which is not asked for. - Insufficient

Statement 1:

We are given that the combined price of 3 oranges and 2 apples is $7:

3(Price of 1 orange)+2(Price of 1 apple)=7
This is a linear equation with two variables. From it alone, we cannot get the unique value of the price of an orange.

Let's take two cases.

1. Say the price of an apple = $1, then the price of an orange is 

2. Say the price of an apple = $2, then the price of an orange is 

No unique value of the price of an orange. Insufficient!

Statement 2:

Merely knowing that the price of an orange and the price of an apple are integers is not sufficient.

Statement 1 & 2 together:

Say the price of an orange = x and the price of an apple = y;

Thus, from Statement 1, we get,

3x + 2y = 7
From Statement 2, we know that the price of an orange and the price of an apple are integers, thus they must be positive. That is,

x ≥ 1
y ≥ 1
Let's assume a few possible integer values of the price of an apple (y) and see whether it results in a unique positive integer value of the price of an orange (x).

We get only one valid value of x, i.e. the price of an orange = $1, a unique value.

So, our analysis has yielded a unique value of x (=1). Sufficient!

We are given that the amount spent on buying Product X, Product Y, and Product Z is $500,000.

Say the amounts spent on buying Product X, Product Y, and Product Z are x,y, and z, respectively.

⇒ x + y + z = 500,000 (Equation 1)

We have to determine whether z>200,000.

Statement 1:

We are given that the sum the trader paid for Product X and Product Y combined was 3 times the sum the trader paid for Product X.

⇒ x + y = 3x
y = 2x (Equation 2)

Substituting equation (2) in equation (1):

⇒ x + 2x + z = 500,000
⇒ 3x + z = 500,000
We have an unknown x. So, we cannot determine whether z > 200,000. Insufficient!

Statement 2:

We are given that the trader paid more to purchase Product Z than to purchase Product Y.

⇒ z > y (Inequality 3)

With the help of equation (1): x + y + z = 500,000 and inequality (3): z > y, we cannot determine whether z > 200,000. Insufficient!

Statement 1 & 2 together:

Let's put down the two equations (1) and (2) and the inequality (3).

x + y + z = 500,000 (Equation 1)

y = 2x (Equation 2)

z > y (Inequality 3)

Since equation (3) has only z and y variables, let's eliminate variable x from equation (1) and (2).

From equation (2), we have x = y/2. By plugging in the value x in equation (1), we get:

y/2 + y + z = 500,000
y + 2y + 2z = 1,000,000
3y + 2z = 1,000,000 (Equation 4)

Substituting (5) in (3):

5z > 1,000,000 
z > 200,000
So, the answer is 'Yes'. The two statements together are sufficient!

Alternate approach:

Alternate way of solving further after Equation (4): 3y + 2z = 1,000,000
Let's assume that y = z, and see what are their values. Say y = z = p
Thus, 3p+2p = 1,000,000
⇒5p = 1,000,000
⇒p = 200,000
Thus, y = z = 200,000;

However, this goes against the fact given in inequality (3): z > y.

Thus, y < 200,000 & z > 200,000. The answer is 'Yes'. Sufficient!

We are given that a teacher gave an equal number of pens, an equal number of pencils, and an equal number of erasers to each student of this class.

You must NOT assume:

(Number of pens per student) = (Numbers of pencils per student) = (Number of erasers per student)

The number of pens that a student - say Student A - got may be different from the number of pencils and from the number of erasers he got; however, every student in the class got as many pens as Student A gets (and likewise, as many pencils and erasers as Student A gets).

Let the total number of students in the class be n, and each student got x number of pens, y number of pencils, and z number of erasers. We have to find out n.

Statement 1:

Each student got pens, pencils, and erasers in the ratio 3:4:5, respectively.

Thus, we have:

x : y : z = 3 : 4 : 5
⇒ x = 3k, y = 4k, z = 5k,where k is a constant of proportionality.
However, we have no information on n. - Insufficient

Statement 2:

We know that the teacher distributed a total of 27 pens, 36 pencils, and 45 erasers.

Thus, nx = 27,ny = 36,nz = 45
We have no information about x, y, z.

Hence, we cannot determine the value of n. - Insufficient

Statement 1 & 2 together:

Substituting the values of x, or y, or z from Statement 1 in the information from Statement 2, we have:

nx = 27 = 3k
n = 9k
Since k is unknown, we cannot determine n.

The valid values of k can be 1, 3, and 9, rendering the values of n = 9, 3, and 1. (k cannot be greater than 9 because n, the number of students, cannot be a fraction. And, k cannot be a fraction, for example, 1/2 etc., because we know that x = 3k, y = 4k, & z = 5k. Since x, y, & z denote the number of items, they cannot be fractions. For x, y, & z to have integer values, k must be an integer.)

No unique value of n. - Insufficient

We have to find out whether 3x − 2y = 0.

Alternatively, we can write 3x − 2y = 0 as x = (2 / 3)y.

Thus, we have to determine whether x = (2 / 3)y.

Statement 1:

We are given that 27x³ − 8y3 = 0.

⇒ 27x³ = 8y³
⇒ x³ = (8 / 27)y³
⇒ x = 2 / 3y; taking the cube root of both the sides. (Remember that the real number x³ has only one real cube root.)

The answer is Yes. - Sufficient!

Statement 2:

We are given that 9x² − 4y² = 0
⇒ 9x² = 4y²
⇒ x² = (4 / 9)y²
⇒ x = ±2 / 3y; taking the square root of both the sides. (Remember that the positive number x² has two square roots, one positive and the other negative.)

If x = (2 / 3)y, the answer is Yes; however, if x = −(2 / 3)y, the answer is No.

No unique value of x. - Insufficient!