All questions of Day 29 for GMAT Exam

(1) x = 2, y is unknown. Insufficient

(2) x and y unknown. Insufficient

(1)+(2) only possibility x=2, y=0; Sufficient

C is correct

In order to determine the main function of the first paragraph, it is helpful to analyze how this paragraph contributes to the entire article. The conclusion and main idea of the passage is that the Dr. Seuss books “revolutionized the children’s book industry”; i.e., they were a significant force of change. The first paragraph sets the stage for that conclusion by establishing the status quo of the early 1950s prior to that change. Be careful: an answer that is merely mentioned in the first paragraph, but does not describe the overall purpose of the paragraph does not qualify as its “main” or primary function. 
(A) The paragraph only describes Fletch’s criticism of the reading primers. It does not describe Fletch’s approach to writing children’s books.
(B) While the paragraph quotes Fletch’s strongly worded description of the “Dick and Jane” primers, this description is not the main or primary function of the paragraph; the description serves to support the more general criticism of the unsatisfactory state of children’s reading education in the early 1950s.
(C) While Fletch’s displeasure with the availability of first- and second-grade level books is mentioned, the paragraph does not directly advocate an increase in children’s books in bookstores. (D) CORRECT. The paragraph starts off by describing the preferred method of teaching reading in the 1950s, and then continues with some strong criticism of this method and the lack of available books in bookstores. By doing so, the author implies that the status quo was not satisfactory and sets the stage for the subsequent events which “revolutionized” the children's book industry. 
(E) While most of the paragraph describes Fletch’s point of view regarding the existing primers and lack of appropriate books in bookstores, the main purpose of the paragraph is not to praise Fletch; his opinions are used to support the overall premise that the status quo at the time was non-satisfactory. 

Before even evaluating the statements, simplify the question. In a more complicated data sufficiency problem, it is likely that some rearranging of the terms will be necessary in order to see the correct answer.
Use the formula for a difference of squares (a2 - b2) = (a + b)(a - b). However, let x2 equal a, meaning a2 = x4.
x4 - y4 = (x2 + y2)(x2 - y2)
Recognize that the expression contains another difference of squares and can be simplified even further.
(x2 + y2)(x2 – y2) = (x2 + y2)(x – y)(x + y)
The question can now be simplified to: "If x and y are distinct positive integers, what is the value of (x2 + y2)(x – y)(x + y)?" If you can find the value of (x2 + y2)(x - y)(x + y) or x4 - y4, you have sufficient data.
Evaluate Statement (1) alone.
Statement (1) says (y2 + x2)(y + x)(x - y) = 240. The information in Statement (1) matches exactly the simplified question. Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) says xy = yx and x > y. In other words, the product of multiplying x together y times equals the product of multiplying y together x times.
The differences in the bases must compensate for the fact that y is being multiplied more times than x (since x > y and y is being multiplied x times while x is being multiplied y times).
4 and 2 are the only numbers that work because only 4 and 2 satisfy the equation n2 = 2n, which is the condition that would be necessary for the equation to hold true.
Observe that this is true: 42 = 24 = 16.
Remember that x > y, so x = 4 and y = 2. Consequently, you know the value of x4 - y4 from Statement (2). So, Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT

We need to find the value of n, given 2(−3⁴ⁿ)=18(27)ⁿ⁺²

(Cancelling 2 on both sides. Also making use of the fact that 3^2k = (-3)^2k)

On questions asking about the main idea of the passage, be sure to refer to the opening paragraph, which usually discusses the main theme of the passage. Also, when selecting your answer, avoid extreme answer choices that describe only a part of the passage or mention information that is beyond the scope of the text. 
(A) This answer choice is directly contradicted by the text. The passage provides an argument for a wider use of the detection mechanisms of insects rather than dogs.
(B) While possible disadvantages involved in using detection mechanisms of dogs are mentioned in the second paragraph, their discussion appears only in one paragraph and thus does not reflect the main idea of the passage.
(C) CORRECT. This answer choice accurately describes the main idea of the passage. Note that this idea permeates the entire passage and conveys the main intention of the author. Also, note that this theme is mimicked in the opening paragraph of the passage: “… recent evidence suggests that insects, rather than mammals, may be used more effectively in this capacity.”
(D) While the second paragraph of the passage is devoted to the discussion of the biological process used by insects to detect odors, this theme is discussed only in one paragraph and fails to reflect the content of the entire passage.
(E) First, the passage mentions only one method (rather than multiple methods): the technique developed by Dietrich Schneider. Secondly, this method is mentioned only in the concluding paragraph of the passage and does not reflect the main theme of the entire text.  

This question asks us to infer something about the “additional responsibilities” described in the third paragraph of the passage. The only information we are given about these “additional responsibilities” is that they are awarded to women who have performed well in a Human Resources capacity, and that they lie outside of the Human Resources department itself. The correct answer choice will be closely tied to one or both of these facts. 
(A) CORRECT. The passage explains, in paragraph two, that women have been strongly associated with the traits and characteristics valued in a Human Resources capacity.  If the "additional responsibilities" are in "other departments," then those responsibilities are likely to be in areas that are less traditionally associated with women than is HR. 
(B) We know only that the departmental responsibilities are not in the Human Resources area; we do not know that the women are taking over, or even merely expanding their responsibilities into, departments that "used to" be run by a man.
(C) The passage indicates that the “additional responsibilities” are given as a reward for strong performance; they may or may not be similar to those that these women have already performed. Indeed, they could very well be new types of responsibilities that are meant to stretch and challenge these executives.
(D) The activity of speaking at industry conferences is explicitly described later in the paragraph as an additional way that women have gained authority and influence.  The wording ("Also...") indicates a new thought compared to the “additional responsibilities” of the previous sentence, rather than an example of those responsibilities.
(E) The passage describes the increasing emphasis on the importance of Human Resources activities to many organizations. The new responsibilities in other departments may or may not be more important, particularly as they are in addition to these women’s prior responsibilities. For example, a successful Human Resources executive could be given the additional responsibility of producing marketing materials for the Company, which may or may not be more crucial to the Company’s success than her earlier responsibilities. 

This is a general question. In order to determine with which statement the author would be most likely to agree, we must determine the author’s main point in writing the passage. A breakdown of the purpose of each paragraph will help. The first paragraph highlights two differing views concerning the roots of jazz music, the second paragraph discusses the diverse origins of jazz, and the third paragraph states the author’s view concerning the origins of jazz: namely, that jazz is truly American because it is rooted in the confluence of West African and European music. More generally, the author believes “that the essence of America lies in the plurality of its roots,” or that to be American is to have a diverse background.
(A) The author believes that jazz should be called an American art form, but not because it was first played in America.  Furthermore, the author believes that because of its origins in Europe and West Africa, not despite these origins. The author believes “that the essence of America lies in the plurality of its roots.” Therefore, it is likely that the author would believe the same about American football, that it is American because of its origins, not despite these origins.
(B) The author believes that jazz should be called an American art form because of its origins in Europe and West Africa. The author believes “that the essence of America lies in the plurality of its roots.” Therefore, it is likely that the author would believe the same about American football, that it is American because of its origins.  Thus, this choice is backward. (C) We have no information about the beliefs of sports scholars.
(D) CORRECT. The author believes “that the essence of America lies in the plurality of its roots.” Therefore, it is likely that the author would believe that the diverse origins of American football make it essentially American.
(E) Because the author believes “that the essence of America lies in the plurality of its roots,” and because American football has diverse origins, the author would be likely to believe that American football should be called an American sport. Thus, this choice is backward. 

In the second paragraph, “scatting” is described as “a technique used by jazz vocalists to mimic the sounds of instruments.” 
(A) CORRECT. A vocalist attempting to vocalize the tone and melodic line just played by a trumpet is an example of a singer mimicking “the sounds of instruments.”
(B) This does not describe “a technique used by jazz vocalists to mimic the sounds of instruments.” 
(C) This is an example of an instrumentalist attempting to imitate the sounds of a vocalist. Scatting is the exact opposite: a vocalist attempting to imitate the sounds of an instrument. 
(D) This does not describe “a technique used by jazz vocalists to mimic the sounds of instruments.”
(E) This does not describe “a technique used by jazz vocalists to mimic the sounds of instruments.” 

Simplify the question by translating it into algebra.
Let P = the total value of John's parting gift
Let E = the amount each associate contributed
Let N = the number of associates
P = NE = 25E
With this algebraic equation, if you find the value of either P or E, you will know the total value of the parting gift.
Evaluate Statement (1) alone.
Two common ways to evaluate Statement (1) alone:
Statement 1: Method 1
Since the question stated that each person contributed equally, if losing four associates decreased the total value of the parting gift by $200, then the value of each associate's contribution was $50 (=$200/4).
Consequently, P = 25E = 25(50) = $1,250.
Statement 1: Method 2
If four associates leave, there are N - 4 = 25 - 4 = 21 associates.
If the value of the parting gift decreases by $200, its new value will be P - 200.
Taken together, Statement (1) can be translated:
P - 200 = 21E
P = 21E + 200
You now have two unique equations and two variables, which means that Statement (1) is SUFFICIENT.
Although you should not spend time finding the solution on the test, here is the solution.
Equation 1: P = 21E + 200
Equation 2: P = 25E
P = P
25E = 21E + 200
4E = 200
E = $50
P = NE = 25E = 25($50) = $1250
Evaluate Statement (2) alone.
Statement (2) says that $1,225 < P < $1,275. It is crucial to remember that the question stated that "25 associates contribute equally to a parting gift for John in an amount that is an integer." In other words P / 25 must be an integer. Stated differently, P must be a multiple of 25.
There is only one multiple of 25 between 1,225 and 1,275. That number is $1,250. Since there is only one possible value for P, Statement (2) is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT, answer D is correct.

"Except" questions require us to test the five answer choices to determine the "odd one out." It is beneficial to use the True / False technique: label each answer choice with a T or an F and look for the odd one out (which, in this case, we should expect to be an F).
(A) CORRECT. False. The second sentence of the second paragraph says of the chemicals that "Both are discharged in high quantities only during waking states." Later sentences tell us that the chemical levels drop during non-REM sleep, not that they disappear completely. 
(B) True. The first sentence of the third paragraph says that "at doses higher than 20 micrograms, [LSD] can have a hallucinogenic effect." This is equivalent to the statement that the dosage will cause hallucinations in some people (otherwise, we could not say that it "can have" a hallucinogenic effect).
(C) True. Sentence four in paragraph two tells us that REM (rapid eye movement sleep) "is associated with dreaming."
(D) True. The third sentence of paragraph three says that the neurons containing norepinephrine "greatly accelerate activity" when LSD is in someone's system. Sentence one of paragraph two tells us that "neurons release norepinephrine" - so if this neuronal activity is increased, then the rate at which norepinephrine is released must also increase. 
(E) True. The last sentence of the second paragraph says that Jacobs hypothesized that "the absence of serotonin was necessary to allow dreaming to occur." 

When answering inference questions, make sure to look for an answer that can be inferred strictly based on the information given in the passage and without making any additional assumptions. Typically, the correct answer will be closely connected to the actual text and directly supported by one or two sentences. 
(A) This statement is directly contradicted by the text of the passage. In the concluding paragraph, the author states that “the detection mechanisms of insects are likely to be applied in practice in the near future,” thus suggesting that they have not been applied in practice to date. (B) The passage provides no information about the time when dogs were first used in the detection of smuggling.
(C) While the last sentence of the second paragraph mentions that signals sent by insects’ receptors allow for “easy detection by researchers,” the passage provides no information about the ease or difficulty of such detection in mammals.
(D) CORRECT. The second sentence of the concluding paragraph states that the technique developed by Dietrich Schneider in the 1950s “became the first method that enabled researchers to record the activity in insect olfactory nerves and identify the compounds that trigger a behavioral response.” Since this technique became the first method, we can infer that no reliable methods had existed prior to the development of this technique, i.e. in the first half of the twentieth century or earlier. 
(E) The passage provides no information regarding the distinctions between flying and crawling insects. 

This is a detail question. On questions of this type, use detail words, such as “an odorant binding protein” to locate the answer in the text. Those words are found in the sentence in the second paragraph that describes the role of this protein: “This protein carries the hydrophobic ligand through the lymph fluid found inside the cell and attaches it to a receptor on the dendritic projections of a sensory nerve cell.”
(A) This answer choice describes the role played by a receptor on the dendritic projections of a sensory nerve cell rather than that played by the odorant binding protein.  
(B) CORRECT. The third sentence in the second paragraph states that “This protein carries the hydrophobic ligand through the lymph fluid found inside the cell and attaches it to a receptor on the dendritic projections of a sensory nerve cell.”
(C) This answer choice describes the role of played by the odorant molecule rather than that played by the odorant binding protein.
(D) This answer choice provides information about the odorant binding protein that is not mentioned in the passage.
(E) While the passage mentions finger-like protuberances in the third paragraph, nothing in the text suggests that it is the odorant binding protein that transmits odors via these protuberances. 

Translate the final sentence, which contains the question, into algebra:
"the number of pages indexed per hour by G-Cache" = X
"greater than three times" translates into: >3
"the number of pages indexed by HTML-Compress" = Y

Putting this together:
Was X > 3Y?
Evaluate Statement (1) alone.
Translate the information from Statement (1) into algebra:
X - Y = 1 million
Since the original question states that "both algorithms indexed a positive number of pages per hour", the following inequalities must hold true:
X > 0
Y > 0
Simply knowing that X - Y = 1 million does not provide enough information to determine whether X > 3Y.
This can be seen via an algebraic substitution or by trying different numbers.
Trying Numbers
Let X = 10 and, therefore, Y = 9
10 is NOT > 3(9)
But, let X = 1.1 and, therefore, Y = .1
1.1 IS > 3(.1)
Algebraic Substitution
X - Y = 1 million
X = Y + 1 million
Plug this into the inequality we are trying to solve for:
Was X > 3Y?
Was (Y + 1 million) > 3Y?
Was 1 million > 2Y?
Was 500,000 > Y?
Was Y < 500,000?

Simply knowing that X - Y = 1 million does not provide enough information to determine whether Y < 500,000
Since different legitimate values of Y produce different answers to the question of whether X > 3Y, Statement (1) is not sufficient.
Statement (1) is NOT SUFFICIENT.
Evaluate Statement (2) alone.
Translate the information from Statement (2) into algebra:
400,000 < Y < 1,400,000
We know nothing about the value of X.
If X were 10 million, the answer to the original question was X > 3Y? would be "yes."
If X were 100,000, the answer to the original question was X > 3Y? would be "no."
Since different legitimate values of X and Y produce different answers to the question of whether X > 3Y, Statement (2) is not sufficient.
Statement (2) is NOT SUFFICIENT.
Evaluate Statements (1) and (2) together.
With the information in Statement (1), we concluded that the original question can be boiled down to:
Is Y < 500,000?
Statement (2) says:
400,000 < Y < 1,400,000
Even when combining Statements (1) and (2), we cannot determine whether Y < 500,000
Y could be 450,000 (in which case X = 1,450,000) or Y could be 650,000 (in which case X = 1,650,000). These two different possible values of X and Y would produce different answers to the question "Was Y < 500,000?" Consequently, we would have different answers to the question "Was X > 3Y?"
Statements (1) and (2), even when taken together, are NOT SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT, Statement (2) alone is NOT SUFFICIENT, and Statements (1) and (2), even when taken together, are NOT SUFFICIENT.

If both x and y are multiples of 11, then both x + y and x - y will be multiples of 11. In other words, if two numbers have a common divisor, their sum and difference retain that divisor.
In case this is hard to conceptualize, consider the following examples:
42 - 18 {both numbers share a common factor of 6}
=(6*7) - (6*3)
=6(7 - 3)
=6(4)
=24 {which is a multiple of 6}

49 + 14 {both numbers share a common factor of 7}
=(7*7) + (7*2)
=7(7+2)
=7*9
=63 {which is a multiple of 7}
However, if x and y are not both multiples of 11, it is possible that x - y is a multiple of 11 while x + y is not a multiple of 11. For example:
68 - 46 = 22 but 68 + 46 = 114, which is not divisible by 11.
The reason x - y is a multiple of 11 but not x + y is that, in this case, x and y are not individually multiples of 11.
Evaluate Statement (1) alone.
Since x-y is a multiple of 22, x-y is a multiple of 11 and of 2 because 22=11*2
If both x and y are multiples of 11, the sum x + y will also be a multiple of 11. Consider the following examples:
44 - 22 = 22 {which is a multiple of 11 and of 22}
44 + 22 = 66 {which is a multiple of 11 and of 22}

88 - 66 = 22 {which is a multiple of 11 and of 22}
88 + 66 = 154 {which is a multiple of 11 and of 22}
However, if x and y are not individually divisible by 11, it is possible that x - y is a multiple of 22 (and 11) while x + y is not a multiple of 11. For example:
78 - 56 = 22 but 78 + 56 = 134 is not a multiple of 11.
Statement (1) alone is NOT SUFFICIENT.
Evaluate Statement (2) alone.
Since the tens digit and the units digit of x are the same, the range of possible values for x includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, x must be a multiple of 11.
Since the tens digit and the units digit of y are the same, the range of possible values for y includes:
11, 22, 33, 44, 55, 66, 77, 88, 99
Since each of these values is a multiple of 11, y must be a multiple of 11.
As demonstrated above, if both x and y are a multiple of 11, we know that both x + y and x - y will be a multiple of 11.
Statement (2) alone is SUFFICIENT.
Since Statement (1) alone is NOT SUFFICIENT and Statement (2) alone is SUFFICIENT.

When answering questions about the overall tone of the passage or attitude of the author, make sure to avoid extreme answer choices. Also, pay close attention to the qualifying words such as “moderately,” “mildly” or “slightly.” These words tone down the following adjective, thus making it more likely to be the correct answer.
(A) CORRECT. The whole passage provides an argument for the increased use of insects’ detection mechanisms. For example, in the second sentence of the first paragraph, the author states that “… insects, rather than mammals, may be used more effectively in this capacity.” Also, the author concludes the passage by saying that “… the detection mechanisms of insects are likely to be applied in practice in the near future.” These statements and the overall tone of the passage suggest that the author is generally optimistic about the use of the detection mechanisms of insects.  
(B) Since the whole passage makes an argument for a wider use of the biological detection systems of insects and discusses their advantages over mammals, the attitude of the author towards them is positive rather than completely neutral.
(C) Throughout the entire passage, the author discusses the advantages of insects’ detection systems and expresses optimism about their potential use in practice. For example, in the second sentence of the first paragraph, the author states that “… insects, rather than mammals, may be used more effectively in this capacity.” Therefore, the attitude of the author cannot be described as highly doubtful.
(D) This answer is likely to be incorrect for the vast majority of GMAT passages. By definition, if the author writes a passage on a certain subject, she is unlikely to be uninterested in the subject area.
 (E) Throughout the entire passage, the author discusses the advantages of insects’ detection systems and expresses optimism about their potential use in practice. For example, the author concludes the passage by saying that “… the detection mechanisms of insects are likely to be applied in practice in the near future.” Therefore, the attitude of the author cannot be described as mildly pessimistic. 

This is a specific question. We should be able to find evidence in the passage to support the truth of four of the answer choices. The “odd man out” will be the correct answer. 
(A) The second paragraph states “the jazz first played in New Orleans in the early 1900s…” 
(B) The third paragraph states “proponents of the argument that jazz is purely American often point to its genesis in New Orleans …” (C) The second paragraph states “jazz ensembles were built predominantly on European instruments, such as the trumpet, trombone, saxophone, and piano.” The trumpet, trombone, and saxophone are horns, and the piano is a stringed instrument.
(D) The second paragraph states that there is an “emphasis on improvisation in jazz music.” 
(E) CORRECT. The passage clearly indicates that some musicologists believe jazz is “the only purely American form of music” while others “argue that jazz is rooted in a history similar to that of America itself, a history of confluence.” The point of disagreement is not whether jazz should be called American, but rather whether jazz should be called “purely” American. The author’s viewpoint is a good example. The author believes jazz comes from a complex convergence of traditions and cultures (not “purely” American). However, the author still believes jazz should be called an American art form: “to deny the rich and complex history of jazz, and the true origins of the art form, is in effect denying the very aspects of the art form that make it undeniably American.”  

The first paragraph introduces two sides of an issue, the second paragraph provides information relevant to the issue, but in a completely objective (or unbiased) manner, and the third paragraph concludes the passage by presenting the author’s take on the issue. 
(A) While the second paragraph presents background information relevant to the issue, it does so in an objective (or unbiased) way, not subjectively. The third paragraph does not “summarize points made earlier in the passage.”
(B) CORRECT. This answer choice correctly describes the structure of the passage.  The first paragraph introduces two differing viewpoints on an issue, the second paragraph objectively presents relevant information, and the third paragraph describes the author’s opinion on the issue.
(C) The second paragraph does not “give a comprehensive history of the debate.” This paragraph gives a brief history of jazz music, but not a history of the debate over the origins of jazz music. Also, “comprehensive” implies a complete and thorough history, an inaccurate description given the brief nature of this passage.
(D) We do not know that the information presented in the second paragraph is “newly discovered information.” Further, the third paragraph does not summarize points made earlier in the passage.
(E) While the first paragraph does present differing viewpoints, it does not necessarily introduce a “controversy.” “Controversy” implies a heated disagreement over an issue; this is a bit too strong given the tone of the passage. Further, even if it were a controversy, the last paragraph doesn’t “settle” anything; it merely gives the author’s opinion on the issue. 

We are asked to find the purpose of the passage. The first paragraph of the passage introduces a theory that seeks to show a link between dreams and hallucinations based upon two chemicals. The second paragraph elaborates on the role of the two chemicals in dreams and the third paragraph does the same for hallucinations. The third paragraph also concludes by noting that the theory remains unproven and would benefit from further testing.
(A) While the passage does outline a theory it does not suggest options for further research; it merely notes that further research would be beneficial.
(B) The author does not act as an advocate, or try to convince the audience of the need for additional research; instead, the author merely notes that further research would be beneficial. 
(C) CORRECT. A "theoretical construct" is equivalent to a theory; the author does introduce a theory that is "inconclusive," or not sufficiently proven.
(D) While the first sentence does imply that research associated with the brain is complex, the rest of the passage does not focus on this topic or attempt to demonstrate the specific complexities involved.
(E) While the passage does articulate a hypothesis, it only presents current research; it does not "lay out the case for proving it." In fact, the last sentence says the hypothesis is "inconclusive."

This is a general question. In order to determine with which statement the author would be most likely to agree, we must determine the author’s main point in writing the passage. A breakdown of the purpose of each paragraph will help. The first paragraph highlights two differing views concerning the roots of jazz music, the second paragraph discusses the diverse origins of jazz, and the third paragraph states the author’s view concerning the origins of jazz: namely, that jazz is truly American because it is rooted in the confluence of West African and European music. More generally, the author believes “that the essence of America lies in the plurality of its roots,” or that to be American is to have a diverse background.
(A) The author believes that jazz should be called an American art form, but not because it was first played in America.  Furthermore, the author believes that because of its origins in Europe and West Africa, not despite these origins. The author believes “that the essence of America lies in the plurality of its roots.” Therefore, it is likely that the author would believe the same about American football, that it is American because of its origins, not despite these origins.
(B) The author believes that jazz should be called an American art form because of its origins in Europe and West Africa. The author believes “that the essence of America lies in the plurality of its roots.” Therefore, it is likely that the author would believe the same about American football, that it is American because of its origins.  Thus, this choice is backward. (C) We have no information about the beliefs of sports scholars.
(D) CORRECT. The author believes “that the essence of America lies in the plurality of its roots.” Therefore, it is likely that the author would believe that the diverse origins of American football make it essentially American.
(E) Because the author believes “that the essence of America lies in the plurality of its roots,” and because American football has diverse origins, the author would be likely to believe that American football should be called an American sport. Thus, this choice is backward.

In working on this question, it is helpful to remember that a number will be divisible by 9 if the sum of its digits equals 9.
Evaluate Statement (1) alone.
Based upon the information in Statement (1), it is helpful to plug in a few values and see if a pattern emerges:
101 - 19 = -9
102 - 19 = 81; the sum of the digits is 9, which is divisible by 9, meaning the entire expression is divisible by 9
103 - 19 = 981; the sum of the digits is 9 + 8 + 1=18, which is divisible by 9, meaning the entire expression is divisible by 9
104 - 19 = 9981; the sum of the digits is 9(2) + 8 + 1=27, which is divisible by 9, meaning the entire expression is divisible by 9
Notice that, in each instance, the sum of the digits is divisible by 9, meaning the entire expression is divisible by 9.
The pattern that emerges is that there are (n-2) 9s followed by the digit 8 and the digit 1.
The pattern of the sum of the digits of 10n - 19 is 9(n-2) + 9 for all values of n > 1. (For n = 1, the sum is -9, which is also divisible by 9.) This means that the sum of the digits of 10n - 19 is 9(n-1). Since this sum will always be divisible by 9, the entire expression (i.e., 10n - 19) will always be divisible by 9.
Based upon this pattern, Statement (1) is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) says that z + 981 is a multiple of 9. This can be translated into algebra: 9(a constant integer) = z + 981
Divide both sides by 9

Since 981 is divisible by 9 (its digits sum to 18, which is divisible by 9), you can further rewrite Statement (2).

Since an integer minus an integer is an integer, Statement (2) can be rewritten even further. Since z divided by 9 is an integer, z is divisible by 9. Statement (2) is SUFFICIENT.

Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT.

Even though lines L and M look parallel and angle BAC looks like a right angle, you cannot make these assumptions.
The formula for the area of a triangle is .5bh
Evaluate Statement (1) alone.
Since EC = 2AC, EA = CA, EC = 2(6) = 12 and line AB is an angle bisector of angle EBC. This means that angle ABC = angle ABE. Since we know that angle ABC = 30, we know that angle ABE = 30. Further, since lines L and M are parallel, we know that line AB is perpendicular to line EC, meaning angle BAC is 90.
Since all the interior angles of a triangle must sum to 180:
angle ABC + angle BCA + angle BAC = 180
30 + angle BCA + 90 = 180
angle BCA = 60
Since all the interior angles of a triangle must sum to 180:
angle BCA + angle ABC + angle ABE + angle AEB = 180
60 + 30 + 30 + angle AEB = 180
angle AEB = 60
This means that triangle BCA is an equilateral triangle.
To find the area of triangle BCE, we need the base (= 12 from above) and the height, i.e., line AB. Since we know BC and AC and triangle ABC is a right triangle, we can use the Pythagorean theorem on triangle ABC to find the length of AB.
6² + (AB)² = 12²
AB² = 144 - 36 = 108
AB = 108^1/2
Area = .5bh
Area = .5(12)(108^1/2) = 6*108^1/2
Statement (1) is SUFFICIENT
Evaluate Statement (2) alone.
The sum of the interior angles of any triangle must be 180 degrees.
DCG + GDC + CGD = 180
60 + 30 + CGD = 180
CGD = 90
Triangle CGD is a right triangle.
Using the Pythagorean theorem, DG = 108^1/2
(CG)² + (DG)² = (CD)²
6² + (DG)² = 12²
DG = 108^1/2
At this point, it may be tempting to use DG = 108^1/2 as the height of the triangle BCE, assuming that lines AB and DG are parallel and therefore AB = 108^1/2 is the height of triangle BCE. However, we must show two things before we can use AB = 108^1/2 as the height of triangle BCE: (1) lines L and M are parallel and (2) AB is the height of triangle BCE (i.e., angle BAC is 90 degrees).
Lines L and M must be parallel since angles FDG and CGD are equal and these two angles are alternate interior angles formed by cutting two lines with a transversal. If two alternate interior angles are equal, we know that the two lines that form the angles (lines L and M) when cut by a transversal (line DG) must be parallel.
Since lines L and M are parallel, DG = the height of triangle BCE = 108^1/2. Note that it is not essential to know whether AB is the height of triangle BCE. It is sufficient to know that the height is 108^1/2. To reiterate, we know that the height is 8 since the height of BCE is parallel to line DG, which is 108^1/2.
Since we know both the height (108^1/2) and the base (CE = 12) of triangle BCE, we know that the area is: .5*12*108^1/2 = 6*108^1/2
Statement (2) alone is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT

In the last paragraph, the author writes: "Establishing a solid framework for understanding the behavior of these indicators helps economists to avoid miscalculations and to guide the country through periods of slow or negative economic growth." 
(A) CORRECT. This choice is consistent with the information contained in the last paragraph. 
(B) This choice focuses only on a subpart of this analysis: the role of the indicators for the private investor.
(C) This choice is not reflected in the passage.
(D) This choice focuses only on downturns whereas the indicators are used for either upward or downward economic change.
(E) This choice is not reflected in the passage. 

We need to find the value of 4m – 2n.

Given expression:

Therefore, 4m -2n =2 * (2m -n) =18

Correct Answer: E

The previous measure to protect the desert tortoise mentioned in the passage is the designation of the species as threatened under the federal Endangered Species Act. The author certainly agrees that the desert tortoise is a threatened species: the second and third paragraphs discuss several problems faced by the species. However, the author believes that the previous efforts have “been insufficient to reverse the species’ decline” (last line of the first paragraph) and that “even with current protections…the desert tortoise faces a tough recovery, so additional measures must be taken” (first line of the last paragraph).
(A) The author is not skeptical of the previous efforts; rather the author agrees with them but feels that they have not gone far enough.
(B) The author feels that the previous efforts to protect the desert tortoise have been insufficient, so while the author may have regard for those efforts, “complete satisfaction” is too strongly worded.
(C) The author does not imply opposition to the previous efforts to protect the desert tortoise; the author agrees with those efforts, but feels that they have been insufficient. 
(D) CORRECT. The author does approve of the designation of the desert tortoise as a threatened species, but qualifies that approval with the assertion that “additional measures must be taken.” 
(E) The author is not disdainful of the previous efforts to protect the desert tortoise; the author supports those efforts, but feels that they have been insufficient. 

The third paragraph states that mortgage applications and profit margins are examples of leading indicators, which have the greatest predictive power. Therefore, we need to find an answer choice that relates to either mortgage applications or profit margins. (A) This choice focuses on the employment rate, which is a coincident indicator (paragraph 2). 
(B) This choice focuses on the number of new homes being built, which is not discussed in the passage. Do not assume that the number of new homes being built can be correlated with mortgage applications, which are indeed a leading indicator (paragraph 3). 
(C) This choice focuses on manufacturing, which is a coincident indicator (paragraph 2). 
(D) CORRECT. Imminent changes in the economic cycle are indicated by leading indicators, of which profit margins are an example (paragraph 3). The increase described in this choice is indeed a profit margin (revenue minus cost).
(E) This choice focuses on bankruptcies, which are not mentioned in the passage. 

This question asks for the main idea of the passage. In order to answer this question, it is useful to identify each topic sentence and then briefly summarize each paragraph of the passage: 
Paragraph 1: The recruitment and development of talent is a growing priority for many organizations. Paragraph 2: This change benefits women, as women run many Human Resources departments, for a number of reasons.  Paragraph 3: Women have benefited from the emphasis on talent development in a number of ways.  
The correct answer choice will incorporate, or at least reference, these ideas.
(A) This answer choice correctly summarizes Paragraph 2 of the passage, but does not reference the increasing importance of talent development or how it has benefited women.  
(B) The passage does not make any claims regarding the relative efficacy of women to men in terms of developing and retaining talent. (C) CORRECT. This answer choice accurately describes the main idea of the passage -- that the increasing emphasis on talent development and recruitment (Paragraph 1) benefits many female executives (Paragraphs 2 and 3).
(D) The passage does not indicate that the rate at which women are being promoted to run Human Resources departments is increasing.
(E) This answer choice correctly summarizes Paragraph 1 of the passage, but fails to mention either women or that women are benefiting from the change described in Paragraph 1.   

The passage cites several factors that negatively impact the desert tortoise population, mainly the threat of predators. The mortality rate would be most likely to decrease if one of those reasons were eliminated.
(A) The passage states that tortoises burrow into the ground for protection from “desert temperature extremes.” The passage does not state that tortoises are only vulnerable to heat. The “desert temperature extremes” may also refer to extreme cold, in which case tortoises burrow to keep warm. Thus, cooler burrows might actually be harmful to the tortoises.
(B) The passage does not mention the mating frequency of desert tortoises. Furthermore, while we might be able to infer that more frequent mating might increase the number of desert tortoise hatchlings, we cannot infer that more frequent mating would reduce the mortality rate of those tortoises.
(C) The vulnerability of hatchling and juvenile tortoises is mentioned, along with the fact that adult tortoises provide no care for their offspring. However, there is nothing in the passage to indicate that adult tortoises could have any positive effect on the survival rate of young tortoises by providing better care for them. It is entirely possible that adult tortoises are simply not equipped to protect the young from predators; feeding and caring for the hatchlings may have no effect on the juvenile survival rate. 
(D) The passage states that females “may only lay eggs when adequate forage is available.” If adequate forage were available, then females will be more likely to lay eggs than they would when forage is scarce. However, the passage does not indicate that the availability of abundant forage plants will make the desert tortoises any more likely to survive once hatched.
(E) CORRECT. The passage states that larger mammalian predators eat desert tortoises when rabbits and rodents are scarce. If rabbits were abundant, such predators would not seek out the desert tortoise, and the mortality rate would likely decrease. 

The question asks us to select the answer choice that best describes the structure of the passage. In order to answer this question, it is useful to identify the topic sentences and summarize each paragraph of the passage: 
Paragraph 1: The recruitment and development of talent is a growing priority for many organizations. Paragraph 2: This change benefits women, as women run many Human Resources departments.
Paragraph 3: Women have benefited from the emphasis on talent development in a number of ways. 
The correct answer choice will reflect this organization.
(A) One could reasonably describe the increased emphasis on talent development and recruitment as “an innovative idea.” However, the first paragraph does not “explain” this idea, as the idea is relatively self-explanatory; the first paragraph instead introduces the change and provides background information. Also, the remainder of the passage does not “list” results, and there is no indication that the impacts resulting from the increased emphasis on talent development and recruitment are “unexpected.”
(B) It might be possible to describe the increased emphasis on talent development and recruitment within many organizations as “a new theory.” However, the remainder of the passage does not present evidence to support this theory; rather, the passage explains and explores the impacts of the increased emphasis on talent development and recruitment.
(C) It is inaccurate to describe the increased emphasis on talent development and recruitment as a “challenge” to “an established practice,” as one would have to frame the previous lack of emphasis as “an established practice.” Also, the passage does not simply document results; paragraph 2 in its entirety explains why the change is having a particular impact.
(D) CORRECT. The first paragraph does introduce a “recent trend,” that organizations are increasingly attentive to the development and recruitment of talent. The second and third paragraphs explain and examine an impact of this trend, in this case the positive effect on some women professionals.
(E) It is possible to describe the increased emphasis of various organizations on talent development and recruitment as a “change of emphasis.” However, the bulk of the passage discusses the impact on women professionals, who are never identified as “advocates” of this change; rather, they are the beneficiaries of the change. 

Given that P is a positive integer and that 1 < P < 30.

We need to find the value of P

Given that P has at least two prime factors.

However, there are more than one composite number between 1 and 30. The possible values of P are:

Clearly, Statement (1) doesn’t lead us to a unique value of P.

Not Sufficient.

Statement 2 says that the cube of P is less than 300.

Let us list out the cubes of natural numbers.

There are 5 natural numbers between 1 and 30 whose cubes are less than 300.

Statement 2 alone is not sufficient to arrive at a unique answer.

From Statement 1,

Possible values of P: 6, 10, 14, 15, 21, 22, 26

From Statement 2,

Possible values of P: 2, 3, 4, 5, 6

By combining the two statements, we get:

P = 6

Therefore statement 1 and statement 2 combined are sufficient to arrive at a unique answer.

Correct Answer: C

Let us first understand the given information.

The question states the following about half-life:

The interesting thing to notice here is that the Half-life apparently is not dependent on the initial mass of the radioactive substance.

In other words, if a particular radioactive substance’s half-life is 2 years, then the time taken by it

 

This makes it easier for us to calculate the time taken by the radioactive substance to decay because we will be simply counting the number of half-lives taken.

We need to find the approximate time taken for a X grams block of the radioactive element to reduce to about X/8 grams.

As we noted earlier,

In 1 half-life, the amount of element left = ½ * X

In 2 half-lives, the amount of element left = ½ * ½ * X = (½)² * X

Let’s say the number of half-lives taken = n.

Then in n half-lives, the amount of element left = (½)ⁿ * X

Given that the mass left is 1/8 th of the original amount.

Therefore amount of element left = X/8

This gives us (½)ⁿ * X = X/8

Therefore the time taken = 3 half-lives = 3*3 = 9 years.

Correct Answer: B

x^y ≥ 1 if one of two things is true. This is when

Note, a negative y does not helps us since any integer raised to a negative power cannot be greater than 1. Hence lets figure out if x and y fulfill one of the two criteria above.

 

1) y = -x

Statement 1 says that y and x are of opposite signs.

Let’s say that x = 2

This means, y = -2

So x^y = 2^-2 = ¼ which is less than 1

Let’s now consider the case x = -2

This means, y = 2

So, x^y = (-2)² = 4, which is greater than 1

Thus, we realize that Statement 1 does not lead us to a definitive answer. So, Statement 1 is NOT SUFFICIENT

 

y = 2^k where k is a non-zero integer

We are given that k cannot be equal to zero.

Can k be a negative integer?

The answer is No. Because if k were to be a negative integer, then y would become a fraction (For example, say k = -3. Then y =2^-3 = 1/8)

But, we are given that y is an integer.

This is only possible if k is a positive integer.

Thus, k can have only positive values and y is a positive multiple of 2.

x may be a positive or a negative integer, but when it is raised to an even power, the result is always going to be positive.

If x = -1 or 1, then the value of x^y will be equal to 1. For any other allowed value of x (remember: x = 0 is not allowed), the value of x^y will be greater than 1.

Statement 2 is SUFFICIENT

 

Given 2² x 8³ = 2 x 4^z

⇒ 2² x 2^3.3 = 2 x 2^2z

⇒ 2¹¹ = 2^1+2z

⇒ 11 = 1 + 2z

⇒10 = 2z

⇒ z = 5

Evaluate Statement (1) alone.
Based upon the formula for the average, you know that:
(5 + x2 + 2 + 10x + 3)/5 = -3
x2 + 10x + 5 + 2 + 3 = -15
x2 + 10x + 5 + 2 + 3 + 15 = 0
x2 + 10x + 25 = 0
(x + 5)2 = 0
x = -5
Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
2) The median of 109, -32, -30, 208, -15, x, 10, -43, 7 is -5
Notice that the given list of numbers has 9 numbers. So median must be the 5th number when all numbers are arranged in increasing order. Median is -5 but none of the numbers are -5. Hence x must be -5. Sufficient alone.
Statement (2) alone is SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is SUFFICIENT

We are given that the scale is an exponential scale. This means that every term on this scale is equal to the previous term multiplied by a fixed value.

We are given that 2^nd term on the scale = 25 = 5²

4^th term on the scale = 625 = 5⁴

From here, we can discern the pattern that:

The nth term on the scale = 5ⁿ

Thus, the 3^rd term on the scale = 5³ = 125

⇒  + 

⇒  + 

⇒  + 

⇒ 

⇒ 

⇒ 8

Evaluate Statement (1) alone.
Substitute the value of x from Statement (1) into the equation and manipulate it algebraically.

Since the question says that y is a positive integer, you know that the cube root of y³, which equals y, will also be a positive integer. Statement (1) is SUFFICIENT.
Evaluate Statement (1) alone (Alternative Method).
For the cube root of a number to be an integer, that number must be an integer cubed. Consequently, the simplified version of this question is: "is x + y² equal to an integer cubed?"
Statement (1) can be re-arranged as follows:
x = y³ - y²
y³ = x + y²
Since y is an integer, the cube root of y³, which equals y, will also be an integer.
Since y³ = x + y², the cube root of x + y² will also be an integer. Therefore, the following will always be an integer:

Statement (1) alone is SUFFICIENT.
Evaluate Statement (2) alone.
Statement (2) provides minimal information. The question can be written as: "is the following cube root an integer?"

If y = 4, x + y² = 2 + 4² = 18 and the cube root of 18 is not an integer. However, if y = 5, x + y² = 2 + 5² = 27 and the cube root of 27 is an integer. Statement (2) is NOT SUFFICIENT.
Since Statement (1) alone is SUFFICIENT and Statement (2) alone is NOT SUFFICIENT

Questions that ask about "primary purpose" must take into account the passage in its entirety. Overall, this passage is about the differing predictive uses of the various economic indicators. 
(A) CORRECT. The passage does indeed focus on the utility of "various economic indicators." 
(B) This choice mistakenly focuses on a process that is not discussed in the passage. 
(C) This choice focuses only on a few sentences in the last paragraph of the passage. 
(D) This choice mischaracterizes the intent of the passage in using the verb "trace", which implies a chronology. 
(E) This choice is incorrect in describing the author's purpose with the verb "to argue." The author does not present an argument in the passage, but rather an objective comparison. 

Paragraph three is about the effects of and research results on lysergic acid diethlyamide, or LSD. 
(A) The passage describes research into Jacob's theory as "promising but inconclusive," but does not make this statement about the drug LSD itself.
(B) CORRECT.  The second sentence of the third paragraph says that "LSD mimics serotonin well enough to... bind at most of [serotonin's] receptor sites."
(C) The passage says that the drug causes the locus ceruleus to accelerate activity, the opposite of the causation suggested by this choice – that the locus ceruleus affects the body’s response to the drug.
(D) The passage states that the drug stimulates norepinephrine but inhibits serotonin. 
(E) The passage says that "at doses higher than 20 micrograms, it can have a hallucinogenic effect."  This means that some people may have hallucinations, but it does not mean that everyone will, as this answer choice suggests.   

The passage discusses several reasons that the desert tortoise is a threatened species. In the second paragraph, the tortoise’s reproductive cycle is discussed, with an emphasis on its low reproductive rate. In the third paragraph, predators such as ravens are discussed. In the final paragraph, the author recommends additional measures to protect the desert tortoise from harm caused by urban expansion and the release of captive tortoises.
(A) In the last paragraph, the author does mention that urban expansion has the unintended effect of increasing the population of ravens, cited in the third paragraph as the primary predator of juvenile tortoises.
(B) The second paragraph discusses the low reproductive rate of desert tortoises as one reason for their population decline and slow recovery.
(C) CORRECT. Although desert temperature extremes are mentioned in the third paragraph, they are cited as a reason that desert tortoises burrow into the earth, not as a reason that the desert tortoise is a threatened species.
(D) The third paragraph discusses several predators of the desert tortoise, specifically ravens.
(E) The release of captive tortoises by pet owners is mentioned in the last sentence of the passage as a danger to the wild tortoise population. 

Lagging indicators have no predictive power. They serve simply as confirmation of the recent state of the economy. Therefore, lagging indicators would not be helpful in determining future courses of action.
(A) This does not require predictive power.
(B) CORRECT. This choice – cutting costs to avoid short-term losses – requires predictive power. And so lagging indicators would not be helpful in determining whether companies should follow this course of action
(C) This does not require predictive power.
(D) This does not require predictive power.
(E) This does not require predictive power. 

The passage mentions the creation of C-level roles such as Chief Talent Officer as an indication that certain organizations are placing a greater emphasis on the recruitment and development of talent. The correct answer choice will reflect this idea. 
(A) Though the passage does indicate that a high proportion of HR departments are led by women, it does not imply that any organization with a Chief Talent Officer employs a woman in the position. 
(B) The passage states only that HR was historically considered of lower importance and the CTO position indicates that HR has increased in stature since that time.  It does not imply that HR is now considered more important that other departments; the increase in stature could merely bring HR into line with other departments.
(C) CORRECT. The passage does imply that the creation of a role such as Chief Talent Officer or Chief Personnel Officer indicates a greater emphasis on the importance of Human Resources. Organizations that have not created analogous positions implicitly have not matched this emphasis.
(D) Although the passage indicates that effective talent recruitment and development are increasingly regarded as bestowing a competitive advantage, the passage does not suggest that organizations with a Chief Talent Officer actually enjoy a competitive advantage relative to other organizations.
(E) Although an organization with a Chief Talent Officer is presented as emphasizing effective Human Resources, the organization may or may not be attractive to prospective female employees overall. For example, the organization may have a record of poor treatment of women, or it could be in an industry that is unattractive to women for other reasons.