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A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture? (A) 2 (B) 2 1/2 (C) 3 (D) 3 1/2 (E) 4 3 parts and 5 parts mean fractions: thus 3 + 5 = 8 or 3/8 + 5/8 thus for 2 gallons you would need 6/8 white and 10/8 black which is 1 gallon for white and 1 gallon plus ½ gallon for black for a total of 2 ½ gallons of paint total. If 4 4x = 1600, then what is (4 x-1 ) 2 ? o Since the answer wants the term in squares it would be best to square both sides also recognize that (4 x-1 ) 2 is equal to 4 2x-2 such as (4 2x ) 2 = 40 2 now the squares cancel with (4 2x ) = 40 now divide both sides by 4 2 and get 4 2x-2 = 2.5 In a certain calculus class, the ratio of the number of mathematics majors to the number of students who are not mathematics majors is 2 to 5. If 2 more mathematics majors were to enter the class, the ratio would be 1 to 2. How many students are in the class? (A) 10 (B) 12 (C) 21 (D) 28 (E) 35

GMAT GRE Questions

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Page 1: GMAT GRE Questions

A certain shade of gray paint is obtained by mixing 3 parts of white paint with 5 parts of black paint. If 2 gallons of the mixture is needed and the individual colors can be purchased only in one-gallon or half- gallon cans, what is the least amount of paint, in gallons, that must be purchased in order to measure out the portions needed for the mixture?

(A) 2(B) 2 1/2(C) 3(D) 3 1/2(E) 4

3 parts and 5 parts mean fractions: thus 3 + 5 = 8 or 3/8 + 5/8 thus for 2 gallons you would need 6/8 white and 10/8 black which is 1 gallon for white and 1 gallon plus ½ gallon for black for a total of 2 ½ gallons of paint total.

If 44x = 1600, then what is (4x-1)2 ?o Since the answer wants the term in squares it would be

best to square both sides also recognize that (4x-1)2 is equal to 42x-2 such as (42x)2 = 402 now the squares cancel with (42x) = 40 now divide both sides by 42 and get 42x-2 = 2.5

In a certain calculus class, the ratio of the number of mathematics majors to the number of students who are not mathematics majors is 2 to 5. If 2 more mathematics majors were to enter the class, the ratio would be 1 to 2. How many students are in the class?

(A) 10

(B) 12

(C) 21

(D) 28

(E) 35

So for example out of a class of 7 students 2 are math and 5 are non-math majors. If there are currently 28 students in the class then are 8 math and 20 non-math majors, and thus if 2

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more math major enter the class then there will be 10 math to 20 non-math which is a ratio of 1 to 2.

The annual rent collected by a corporation from a certain building was x percent more in 1998 than in 1997 and y percent less in 1999 than in 1998. Was the annual rent collected by the corporation from the building more in 1999 than in 1997?

(1)x>y(2)xy/100 < x-y

So say for example in 1998 it was 110 (x is 10 percent) and 1997 it was 100, and in 1999 it was 88 (y is 20 percent) and 1998 was 110. No because in 1999 it was 88 and in 1997 it was 100. [1] is not sufficient because for example if x is 20 percent and y is 18 percent then 1997>1999, however if x is 20 percent and y is 10 percent then 1999>1997, thus you get conflicting answers. [2] shows that for the expression to be true x must always be greater than y by a margin of 3.4 or greater if that margin is less than 3.4 than the expression doesn’t hold true. And for x-y margins 3.4 and greater (such as x is 20 percent and y is 16.6 percent) 1999>1997 always.

If n is greater than 1, is n equal to 2?1) n has exactly 2 positive factors2) the difference of any two distinct positive factors of n are odd.

o [1] N could be 3 or 5 which is not equal to 2 thus [1] gives conflicting answer [NOT SUFFICIENT], [2] is sufficient because if n is 2 then its factors 2 and 1 when subtracted give 1 which is odd, thus [2] is sufficient to say that n is equal to 2.

If n is a positive integer, is (1/10)^n<0.01?1) n >22) (1/10)^n-1<0.1

o [1] if n is 3 then 1/1000 is less than 0.01 and for every n greater than 2 the result will be less than 0.01 thus [1] is [SUFFICIENT] , [2] says that the minimum that n can be is 3 and if n is 3 then (1/10)^n<0.01 is true thus [2] is also [SUFFICIENT].

What is the least such that is divisible by 1000?(A) 8(B) 10(C) 15

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(D) 20(E) 25

o For example try 10! Which is 10*9*8*7*6*5*4*3*2*1/1000 gives 9*8*7*3*2*1/5 which is not an integer because none of the numerators are divisible by 5, on the other hand 15! 15*14*13*12*11*10*9*8*7*6*5*4*3*2*1/1000 is divisible by 1000 because 1000 cancels out from the denominators by the numerator

Is point closer to point than to point ?

1. Point lies on the line 2. Point lies on the line

, , and are points on the plane. Is ? 1. 2.

What is the last digit of ?(A) 1(B) 3(C) 6(D) 7(E) 9

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The safety distance (meters) between cars moving on a motorway depends on their speed (meters per second):

If two cars want to maintain a time interval of 1 second between each other, which of the following speeds will breach the safety regulation?(A) 5 m/s(B) 10 m/s(C) 25 m/s(D) 50 m/s(E) 90 m/s

All pages of the book are numbered. If the first page is numbered 1 and the last page is numbered 705, on how many pages does digit 9 appear in the numeration?

(A) 70(B) 77(C) 126(D) 133(E) 140

If the circus were to sell all of its 220 tickets for this month's performance at its usual price, the revenue from sales would be 10% greater than that collected last month. If the circus raised the ticket price by 5% and sold only 200 tickets as a result, what percent less would last month's revenue be compared to this month's revenue(A) 2(B) 5

(C)

(D)

(E)

If x^2 - y^2 = 27, what is the value of (x + y)^2?

(1) y = 3

(2) x - y = 3

(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.

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(D) EACH statement ALONE is sufficient.

(E) Statements (1) and (2) TOGETHER are NOT sufficient

For the above question recognize the trick/trap: A box contains 10 light bulbs, fewer than half of which are defective.

Two bulbs are to be drawn simultaneously from the box. If n of the bulbs in box are defective, what is the value of n? (1) The probability that the two bulbs to be drawn will be defective is 1/15. (2) The probability that one of the bulbs to be drawn will be defective and the other will not be defective is 7/15.

Is the product of and equal to 1?

1. 2. Ans: E

--> --> --> either or . Two different answers, not sufficient.

--> --> --> either or . Two different answers, not sufficient.

There are two concentric circles with radii 10 and 8. If the radius of the outer circle is increased by 10% and the radius of the inner circle decreased by 50%, by what percent does the area between the circles grow?

(A) 140%(B) 141%(C) 190%(D) 192%(E) 292%

If Dave works alone he will take 20 more hours to complete a task than if he worked with Diana to complete the task. If Diana works alone, she will take 5 more hours to complete the complete the task, then if she worked with Dave to complete the task? What is the ratio of the time taken by Dave to that taken by Diana if each of them worked alone to complete the task?

A. 4 : 1

B. 2 : 1

This question has a trap figure out the trap

This question has a trap figure out the trap cannot just add hours e.g. if the Dave and Diana work together at 20 hours it cannot be Dave = 20+30 and Diana = 20+5

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C. 10 : 1

D. 3 : 1

E. 1 : 2 Venn Diagram problem equation: Total number of students in the

3/2 circles = n [number of students]+ x [number of students in 2 circles] + 2y [y is the number of students in 3 circles]

In a class of 100 students, 46 passed in English, 46 passed in Math and 58 passed in Commerce. The number who passed in English and Math is 16, Math and Commerce is 24 and English and Commerce is 26, and 7 passed in all three subjects. How many failed in all the subjects? Ans: 9

Of the 300 patients who suffered from at least one symptom of A, B, and C, 35% suffered from A, 45% suffered from B, 40% suffered from C, 10% suffered from exactly 2 of them. How many people suffered from exactly one symptom? 255

According to the directions on a can of frozen orange juice concentrate, 1 can of concentrate is to be mixed with 3 cans of water to make orange juice. How many 12-ounce cans of the concentrate are

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required to prepare 200 6-ounce servings of orange juice? A. 25 B. 34 C. 60 D. 67 E. 100

A certain restaurant offers 6 kinds of cheese and 2 kinds of fruit for its dessert platter. If each dessert platter contains an equal number of kinds of cheese and kinds of fruit, how many different dessert platters could the restaurant offer? A) 8 B) 12 C) 15 D) 21 E) 27

Mrs. Napueta has been given film vouchers. Each voucher allows the holder to see a film without charge. She decides to distribute them among her four nephews so that each nephew gets at least two vouchers. How many vouchers has Mrs. Napueta been given if there are 120 ways that she could distribute the vouchers?(A) 13

(B) 14

(C) 15

(D) 16

(E) more than 16Formula - Number of ways of distributing n identical things among r persons when each person may get any number of things = C (n+r-1, r-1), Using the formula above we get = C(n-8+4-1, 3) = (n-8+4-1)C3 = 120 = (n-5)(n-6)(n-7) = 120 * 3! = 720

1. For 3 sets A, B, and C: P(AuBuC) = P(A) + P(B) + P(C) – P(AnB) –

P(AnC)–P(BnC)+P(AnBnC)

2.No of persons in exactly one set:

P(A) + P(B) + P(C) – 2P(AnB) – 2P(AnC) – 2P(BnC) + 3P(AnBnC)

3. No of persons in exactly two of the sets: P(AnB) + P(AnC) + P(BnC) –

3P(AnBnC)

This question has a trap figure out the trap do not pick 12

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4. No of persons in exactly three of the sets: P(AnBnC)

5. No of persons in two or more sets: P(AnB) + P(AnC) + P(BnC) –

2P(AnBnC)

6.No of persons in at least one set:

P(A) + P(B) + P(C) - P(AnB) - P(AnC) - P(BnC) + 2 P(AnBnC)

A boat traveled upstream a distance of 90 miles at an average speed

of (v-3) mph and then traveled the same distance downstream at an

average speed of (v+3) mph. If the trip upstream took half an hour

longer than the trip downstream, how many hours did it take the boat

to travel downstream?

(A)2.5

(B)2.4

(C)2.3

(D)2.2

(E) 2.1

Edwin is planning to drive from Boston to New Orleans. By what percent would his travel time be reduced if Edwin decides to split the driving time equally with his friend George, instead of making the trip alone?(1) The driving distance from Boston to New Orleans is 1500 miles.(2) George’s driving speed is 1.5 times Edwin’s driving speed.

Stephanie, Regine, and Brian ran a 20 mile race. Stephanie and Regine's combined times exceeded Brian's time by exactly 2 hours. If nobody ran faster than 8 miles per hour, who could have won the race?

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I. Stephanie II. Regine III. Brian (A) I only(B) II only(C) III only(D) I or II only(E) I, II, or III

The vertical position of an object can be approximated at any given time by the function: p(t) = rt – 5t2 + b where p(t) is the vertical position in meters, t is the time in seconds, and r and b are constants. After 2 seconds, the position of an object is 41 meters, and after 5 seconds the position is 26 meters. What is the position of the object, in meters, after 4 seconds?(A) 24(B) 26(C) 39(D) 41(E) 45

A hiker walking at a constant rate of 4 miles per hour is passed by a cyclist traveling in the same direction along the same path at a constant rate of 20 miles per hour. The cyclist stops to wait for the hiker 5 minutes after passing her, while the hiker continue to walk at her constant rate. How many minutes must the cyclist wait until the hiker catches up?A. 20/3 B. 15 C. 20 D. 25 E. 80/3

One smurf and one elf can build a treehouse together in two hours, but the smurf would need the help of two fairies in order to complete the same job in the same amount of time. If one elf and one fairy worked together, it would take them four hours to build the treehouse. Assuming that work rates for smurfs, elves, and fairies remain constant, how many hours would it take one smurf, one elf, and one fairy, working together, to build the treehouse?(A) 5/7

(B) 1

(C) 10/7

(D) 12/7

Double check problem, very tricky problem, answer is not 25

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(E) 22/7

A paint crew gets a rush order to paint 80 houses in a new development. They paint the first y houses at a rate of x houses per week. Realizing that they'll be late at this rate, they bring in some more painters and paint the rest of the houses at the rate of 1.25x houses per week. The total time it takes them to paint all the houses under this scenario is what fraction of the time it would have taken if they had painted all the houses at their original rate of x houses per week?(A) 0.8(80 – y)(B) 0.8 + 0.0025y(C) 80/y – 1.25(D) 80/1.25y(E) 80 – 0.25y

Linda and Angela contract to paint a neighbor's house. Even though Lindaspends 50% more time painting the house than Angela, each receives a paymentof m dollars when the work is completed. If Angela decides to pay Linda ndollars so that they would have received the same compensation per hourworked, what is n in terms of m?A)(1/2)mB)(1/3)mC)(1/4)mD)(1/5)mE)(1/6)m

The end of a blade on an airplane propeller is 10 feet from the center. If the propeller spins at the rate of 1,320 revolutions per second, how many miles will the tip of the blade travel in one minute? (1 mile = 5,280 feet) A. 200 pi B. 240 pi C. 300 pi D. 480 pi E. 1,200 pi

How many distinct prime divisors does a positive integer have?1. Has one prime divisor2. has one prime divisor [Ans: C]

Very tricky question, pay very close attention

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p = 16, q = 9, what is the area of ᐃABC

A vessel contains milk and water in the ratio 3:2. The volume of the contents is increased by 50% by adding water to this. From this solution 30 litre of the mixture is withdrawn and then replaced with water. The resultant ratio of milk to water in the final solution is 3:7. Find the original volume of the solution?

In its most recent approach, the comet Crommelin passed the Earth at about the same distance and in about the same position, some 25 degrees above the horizon, that Halley’s Comet will pass the next time it appears.(A) that Halley’s comet will pass(B) that Halley’s comet is to be passing(C) as Halley’s comet(D) as will Halley’s comet(E) as Halley’s comet will do

Except for one class in history and one in biology, all the student's graduation requirements have been fulfilled.(A) Except for one class in history and one in biology, all the student's graduation requirements have been fulfilled.(B) Except for needing to take one class in history and one in biology, the student has fulfilled all of his requirements for graduation.(C) The student has fulfilled all his graduation requirements except for one class in history and one in biology.(D) Except for one history class and one biology class, the student has fulfilled all of his graduation requirements.(E) Aside from the history class and biology class that he needs to take, the student's graduation requirements have all been fulfilled.

We now have wireless computer networks, direct-broadcast satellite television, digital wireless cable television networks, global telephone service, and global positioning systems that can pinpoint an

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individual’s location to a few inches.A. that can pinpoint an individual’s location to a few inchesB. that can pinpoint an individual’s location in a few inchesC. which can pinpoint an individual’s location to a few inchesD. which can pinpoint an individual’s location of a few inchesE. which should pinpoint an individual’s location to a few inches

o Rule: A comma must always come before the word 'which'. Only answer choices that remain are A and B.

The skill and the precision of the Anasazi, ancient inhabitants of the Southwest, in measuring the movements of the Sun and Moon is evidenced not only at Chaco Canyon but at a number of other sites.(A) in measuring the movements of the Sun and Moon is evidenced not only at(B) in measuring the movements of the Sun and Moon are evidenced not only at(C) in measuring the movements of the Sun and Moon is evidenced at not only(D) to measure the movements of the Sun and Moon is evidenced at not only(E) to measure the movements of the Sun and Moon are evidenced not only at

o Idiom: skill in (doing something), e.g. Skill in sailing; Skill in shooting etc.The skill and the precision of Anasazi (Two qualities of Anasazi) = Pluralso IS is OUT and ARE is IN.

Although it was once funded entirely by the government, the Victoria and Albert Museum was one of the first of Britain’s national museums seeking support from corporations and private donors and to increase income by increasing attendance.(A) one of the first of Britain’s national museums seeking support from(B) one of Britain’s first national museums seeking support of(C) among Britain’s first national museums to seek support of(D) among the first of Britain’s national museums to seek support from(E) among Britain’s first national museums that have sought the support of

o to seek support....to increase....parallelism To rely on anecdotal evidence of social phenomena is ignoring decades

of increasing sophistication in the use of statistics in sociology.

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A. To rely on anecdotal evidence of social phenomena is ignoringB. To rely on anecdotal evidence of social phenomena is to ignoreC. To rely on anecdotal for demonstration of social phenomena is ignoringD. Relying on anecdotal evidence of social phenomena is to ignoreE. Relying on anecdotal evidence of social phenomena amounts to the ignoring of

o B. This one is pretty straightforward parallelism: to do x is to do y.

In 1990’s, there are more babies born by women over thirty years old than under it.(A) than under it(B) than were they under it(C) than had been under it(D) than were the babies(E) than those were under it

According to a recent research study, more than 90% percent of graduates of private high schools in a certain county continue their education in college. By contrast, only 65% of graduates of public high schools subsequently pursue college education. Therefore, if parents in the county wish to increase the likelihood that their children will attend college, they should send them to private rather than public schools. Which of the following statements would most seriously weaken the argument above? (A) Graduates of private schools typically score higher on standardized tests and other tests of academic achievement. (B) While private schools are typically very expensive, attendance of public school is free for the residents of the county. (C) In comparison with graduates of private schools, a substantially greater proportion of public school graduates receive need-based financial aid for their college education. (D) In comparison with private schools, public schools provide more opportunities for student involvement in sports and other athletic activities, which almost always increase the likelihood of students’ acceptance to colleges. (E) Since most public schools are located in rural areas of the county populated primarily by farmers, nearly 30% of students from public high schools choose to pursue farming occupations rather than apply to colleges.

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No matter how much work it may require. getting an MBA turns out to be a wiseinvestment for most people.Even though it requires much work

The driver took the people for a ride who had been waiting.the people who had been waiting for a ride

Rising costs to raw materials may impel us to rise prices farther .costs of raw materials may impale us to raise prices further

She is the most dedicated gardener on the block, every day watering the more than 50plants in her yard.Every day watering more than the 50 plants in her yard

o “the more than 50” refers to more than 50 plantso “more than the 50 plants” refers to more than just

watering the plants also such as trimming or other activities

Hector remembers San Francisco as it was when he left ten years ago.As though he had left ten years ago

Students at Carver High School are encouraged to pursue extracurricular activities likestudent government. sports. and the arts.Activities such as student government, sports, and the arts

In the waning days of the emperor's life, the conquest of new lands on the borders of the empire was/were considered vital. here we can ask the questions what is the conquest of? New lands thus is the prepositional phrase, the subject in this case is “the conquest” which is singular.

The tidal forces to which an object falling into a black hole is/are subjected is/are sufficient to tear the object apart.

o What is the object subjected to? Tidal forces (prepositional phrase), thus object which is singular is the subject

The board is investigating several executives' compensation packages in order to determine how much may have been improperly awarded to THEM.

o In this sentence, the pronoun them actually refers better to packages than to executives'. In fact, according to the Possessive Poison rule, them cannot refer to executives'. The Possessive Poison rule states that possessive nouns can serve as antecedents only to possessive pronouns, not to subject or object pronouns.

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Use who, whom, whose to modify people, use which and that to modify things

PRESENT PERFECT: HAVE/HAS + PAST PARTICIPLEo If you use since, you must use the Present Perfect to

indicate continued action or effect: Since 1986 no one HAS BROKEN that world record.

Future to Conditional “will” to “would” The scientist BELIEVES [Present] that the machine Will BE

[Present] wonderful. The scientist BELIEVED [Past] that the machine Would BE

[Conditional Tense] wonderful. MGMAT Sentence Correction if…then rules pg. 106 The subjunctive construction with a Bossy Verb is always as

follows:Bossy Verb + THAT + subject + Command SubjunctiveWe PROPOSE THAT the school board DISBAND.

Take note of the following incorrect constructions, all commonly tested on the GMAT:Wrong: We PROPOSE the school board DISBAND. (That is not optional.)Wrong: We PROPOSE THAT the school board DISBANDS.Wrong: We PROPOSE THAT the school board IS TO DISBAND.Wrong: We PROPOSE THAT the school board WILL DISBAND.

Wrong: We PROPOSE THAT the school board SHOULD DISBAND. LIKE her brother. Ava aced the test. [Nouns with no verbs] AS her brother DID. Aya aced the test. [Nouns with verbs

(DID)] The preposition unlike is used to show a contrast between two

nouns: Unlike John, Mary likes cookies. The sentence above is saying that Mary is unlike John. A contrast is being made between the noun Mary and the noun John. The conjunction whereas is used to show a contrast between two clauses. A clause contains both a subject (noun) and a verb. Whereas Mary likes cookies, John prefers ice cream. The sentence above is showing a contrast not just between the noun Mary and the noun John but between the entire clause Mary likes cookies and the entire clause John prefers ice cream.

Some who favor putting governmental enterprises into private hands suggest that conservation objectives would in general be better served if private environmental groups were put in charge of operating and financing the national park system, which is now run by the government.

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Which of the following, assuming that it is a realistic possibility, argues most strongly against the suggestion above?(A) Those seeking to abolish all restrictions on exploiting the natural resources of the parks might join the private environmental groups as members and eventually take over their leadership.(B) Private environmental groups might not always agree on the best ways to achieve conservation objectives.(C) If they wished to extend the park system, the private environmental groups might have to seek contributions from major donors and general public.(D) There might be competition among private environmental groups for control of certain park areas.(E) Some endangered species, such as the California condor, might die out despite the best efforts of the private environmental groups, even if those groups are not hampered by insufficient resources.

Choi: All other factors being equal, children whose parents earned doctorates are more likely to earn a doctorate than children whose parents did not earn doctorates.Hart: But consider this: Over 70 percent of all doctorate holders do not have a parent that also holds a doctorate.Which of the following is the most accurate evaluation of Hart’s reply?(A) It establishes that Choi’s claim is an exaggeration.(B) If true, it effectively demonstrates that Choi’s claim cannot be accurate.(C) It is consistent with Choi’s claim.(D) It provides alternative reasons for accepting Choi’s claim.(E) It mistakes what is necessary for an event with what is sufficient to determine that the event will occur.

In the next four years, the number of doctors, nurses, and other health care workers will increase significantly worldwide. Even so, the average compensation received by such professional will not decline but rather is likely to increase. This is due, at least partly, to the fact that the median age of the world’s population will increase steadily in this same period of time.The argument above depends logically upon which of the following assumptions?(A) The increase in the number of health care workers will be responsible for the increase in the average life span (B) The compensation of doctors and physical therapists who treat the elderly will increase more than that of other health care workers(C) As a group, older people receive more attention from health care workers than do younger people. (D) Geriatrics, a branch of medicine focusing on the health problems of older people, is the most expensive element of American health care.

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(E) Increase in the median age of the population will occur in all regions of the world.

Before the advent of writing each of the isolated clans of the Comaquogue tribe had master storytellers whose function was to orally transmit the clan's tradition from one generation to the next. When writing was developed within certain clans of the tribe, their master storytellers disappeared within a few generations. This stands to reason, since the availability of written records obviated the need for masterful oral communicators to keep the tradition of literate clans alive. What has puzzled anthropologists, however, is the total lack of masterful storytellers in modern illiterate Comaquogue clans.Which of the following, if true, best helps to explain the puzzling situation mentioned above?(A) Modern illiterate Comaquogue clan members display personality semble their ancestors more closely than they characteristics that resemble their ancestors more closely than they resemble the characteristics of modern literate Comaquogue clan members.(B) Modern illiterate Comaquogue clans participate in more ritual gatherings than most modern literate Comaquogue clans do, but they participate in fewer ritual gatherings than did their common ancestors.(C) Modern illiterate Comaquogue clans are recently descended from long-time literate clans that failed to pass on the skills of reading and writing due to a devastating 75-year war.(D) The celebrations of modern illiterate Comaquogue clans involve a great deal of singing and dancing, and children are taught clan songs and dances from a very young age.(E) The traditions of modern illiterate Comaquogue clans are an amalgamation of the cumulative experiences of previous generations plus innovations to the heritage added by the current generation of clan members.

Historian: Newton developed mathematical concepts and techniques that are fundamental to modern calculus. Leibniz developed closely analogous concepts and techniques. It has traditionally been thought that these discoveries were independent. Researchers have, however, recently discovered notes of Leibniz’ that discuss one of Newton’s books on mathematics. Several scholars have argued that since the book includes a presentation of Newton’s calculus concepts and techniques and since the notes were written before Leibniz’ own development of calculus concepts and techniques, it is virtually certain that the traditional view is false. A more cautious conclusion than this is called for, however. Leibniz’ notes are limited to early sections of Newton’s book, sections that precede the ones in which Newton’s calculus concepts and techniques are presented.In the historian’s reasoning, the two boldfaced portions play which of

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the following roles?A. The first provides evidence in support of the overall position that the historian defends; the second is evidence that has been used to support an opposing position.B. The first provides evidence in support of the overall position that the historian defends; the second is that position.C. The first provides evidence in support of an intermediate conclusion that is drawn to provide support for the overall position that the historian defends; the second provides evidence against that intermediate conclusion.D. The first is evidence that has been used to support a conclusion that the historian criticizes; the second is evidence offered in support of the historian’s own position.E. The first is evidence that has been used to support a conclusion that the historian criticizes; the second is further information that substantiates that evidence.

Federal regulations require that corporations use separate accounting firms for audit and non-audit services. This presents difficulties for many multi-national companies because there are only four large international accounting firms based in the United States. An outspoken group of CEOs has suggested breaking up the “Big Four” firms into smaller operations, so that corporations will have more options for their accounting needs.Which of the following stipulations would be most helpful in assuring the success of the CEOs’ plan to provide more variety in accounting services by breaking up the Big Four firms?(A) The firms should maintain their multi-national contacts.(B) CEOs for the new companies should be chosen from inside each firm.(C) Corporations must keep the same firm for their audit services, but should choose a new firm for non-audit needs.(D) The new firms should maintain their internal audit procedures.(E) The Big Four firms should divide so that the audit and non-audit sections are not broken up.

22. In recent years cattle breeders have increasingly used crossbreeding, in part that their steers should acquire certain characteristics and partly because crossbreeding is said to provide hybrid vigor. A) in part that their steers should acquire certain characteristics B) in part for the acquisition of certain characteristics in their steers

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C) partly because of their steers acquiring certain characteristics. D) Partly because certain characteristics should be acquired by their steers. E) Partly to acquire certain characteristics in their steers.

Contemporary accounts of the life of Charlemagne, crowned emperor by the pope in 800, show that the founder of the Carolingian renaissance in literature and the arts was himself an illiterate driven by his desire for a civilized state to reform education in his kingdom.a) that the founder of the Carolingian renaissance in literature and the arts was himself an illiterate driven by his desireb) that the founder of the Carolingian renaissance in literature as well as in the arts was himself an illiterate and also driven by his desirec) that the founder of the Carolingian renaissance in literature and the arts was himself an illiterate and that he was driven by his desired) that the founder of the Carolingian renaissance in literature as well as in the arts was himself an illiterate and that he was driven by his desiree) that the founder of the Carolingian renaissance in literature and the arts was himself an illiterate and that his desire drove him

A glance at the answer choices suggests that the issue here involves the participle “ driven. ” The sentence gives the surprising detail that a person interested in literature was illiterate, and then explains why an illiterate would have such an interest. As such, the participle “ driven ” is an integral description of the word “ illiterate, ” not of the man in general. Therefore, the participle must stand as it is and choice (A) is correct. Each other choice separates illiterate from driven, altering the meaning of the sentence

A driver's license in one country is not always enough to enable a person to drive in another country legally. A) A driver's license in one country is not always enough to enable a person to drive in another country legally [A driver’s license cannot enable a person – it can only be used for driving, not enabling anybody]B) It is not always enough to have a driver's license in one country in order to drive in another country legally C) It is not always enough to have a driver's license in one country for driving in another country legally D) Having a driver's license in one country, it is not always enough in order to drive in another country legally E) A driver's license in one country is not always enough for driving in another country legally

Even though the costs of paying baseball players amounts to a sum greater than one half of overall cost of operating a Major League

Very tricky question, pay very close attention

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Baseball team last year, Major League Baseball franchise owners were still willing to pay increasingly higher salaries to top players.A. amounts to a sum greaterB. amounts to moreC. amounted to more ["A sum" in the given context refers to a singular measure, a collective noun that acts as a singular and hence the right comparative degree of adjective will be the “more” normally used for the non-countable]D. amounted to a greater sumE. amounted to greater

Almost like clones in their similarity to one another, the cheetah species’ homogeneity makes them especially vulnerable to disease.

(A) the cheetah species’ homogeneity makes them especially vulnerable to disease (B) the cheetah species is especially vulnerable to disease because of its homogeneity(C) the homogeneity of the cheetah species makes it especially vulnerable to disease (D) homogeneity makes members of the cheetah species especially vulnerable to disease (E) members of the cheetah species are especially vulnerable to disease because of their homogeneity

Deliberately imitating the technique of Louis Armstrong, jazz singer Billie Holiday’s approach to singing was to use her voice like an instrument, in that she ranged freely over the beat, flattened out the melodic contours of tunes, and, in effect, recomposed songs to suit her range, style, and artistic sensibilities.(A) Billie Holiday’s approach to singing was to use her voice like an instrument, in that she ranged freely over the beat, flattened(B) Billie Holiday’s approach to singing was to use her voice in a similar way to how other musicians play instruments, in ranging freely over the beat, flattening(C) Billie Holiday approached singing by using her voice like other musicians played instruments, ranging freely over the beat, flattening(D) Billie Holiday used her voice in the same way that other musicians use their instruments, in that she ranged freely over the beat, flattening(E) Billie Holiday approached singing by using her voice like other musicians Instruments, ranging freely over the beat, flattening Billie Holiday’s approach to singing was to use her voice like

an instrument,in that she ranged freely over the beat, flattened. – As we

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are comparing Armstrong with Holiday’s approach and the singing process is continuous hence flattened is wrong.B. Billie Holiday’s approach to singing was to use her voice in a similar wayto how other musicians play instruments, in ranging freely over the beat,flattening.- - as we are comparing Armstrong with Holiday’s approach and the singing process is continuous hence flattened is wrong.C. Billie Holiday approached singing by using her voice like other musiciansplayed instruments, ranging freely over the beat, flattening. – who is ranging freely over beat the musicians or Billie not clear. Hence out. D. Billie Holiday used her voice in the same way that other musicians use theirinstruments, in that she ranged freely over the beat, flattening. – very clear wording and meaning. E. Billie Holiday approached singing by using her voice like other musiciansInstruments, ranging freely over the beat, flattening. – problem with billing using her voice like other played instruments.

According to a recent magazine article, of those office employees who typically work 8 hours at the office each day but sometimes say that they will work at home on a particular day, 25 percent actually work less than one hour. At the same time, over 90 percent of those same office employees believe they are more productive working at home than working in their office.

The statements above, if true, best support which of the following conclusions about the office employees discussed in the article?

(A) On average, the office employees working at home for a day work fewer hours than office employees working at the office.(B) 10 percent of the office employees are less productive working from home than working in their office.(C) At least 15 percent of the office employees do not define productivity exclusively in terms of the number of hours worked. [25% of 90 is 22.50, so at least 15% believe that

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getting the job done doesn’t depend on the number of hours worked](D) At least 25 percent of the office employees can complete the same amount of work in one hour at home as in 8 hours at the office.(E) Some of the office employees make statements regarding their productivity that are not in fact true.

Among lower- paid workers, union members are less likely than non union members to be enrolled in lower- end insurance plans imposing stricter limits on medical services and requiring doctors to see more patients, and spend less time with each.

(A) imposing stricter limits on medical services and requiring doctors to see more patients, and spend(B) imposing stricter limits on medical services , requiring doctors to see more patients, and spending(C) that impose stricter limits on medical services, require doctors to see more patients, and spend(D) that impose stricter limits on medical services and require doctors to see more patients, spending [there are 3 activities a)impose stricter limits on medical services b) require doctors to see more patients, and c) spend less time with each.in these a and b are independent and c is dependent on b.... C makes all a ,b ,c independent...... E makes b and c dependent on a..only D makes a and b are independent and c dependent on b.. therefore D is the ans...](E) that impose stricter limits on medical services, requiring doctors to see more patients and spending

The frequently expressed view that written constitutions are inherently more liberal than unwritten ones is false. No written constitution is more than a paper with words on it until those words are both interpreted and applied. Properly understood, then, a constitution is the sum of those procedures through which the power of the state is legitimately exercised and limited. Therefore, even a written constitution becomes a liberal constitution only when it is interpreted and applied in a liberal way.

If the statements in the argument are all true, which one of the following must also be true on the basis of them?(A) A careful analysis of the written text of a constitution can show that the constitution is not a liberal one.(B) It is impossible to determine that a written constitution is liberal merely through careful analysis of the written text.

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(C) There are no advantages to having a written rather than an unwritten constitution.(D) Constitutions that are not written are more likely to be liberal than are constitutions that are written.(E) A constitution is a liberal constitution if it is possible to interpret it in a liberal way.

Student Advisor: One of our exchange students faced multiple arguments with her parents over the course of the past year. Not surprisingly, her grade point average (GPA) over the same period showed a steep decline. This is just one example of a general truth: problematic family relationships can cause significant academic difficulties for our students.

Which of the following is an assumption underlying the general truism claimed by the Student Advisor?(A) Last year, the exchange student reduced the amount of time spent on academic work, resulting in a lower GPA.(B) The decline in the GPA of the exchange student was not the reason for the student's arguments with her parents.(C) School GPA is an accurate measure of a student's intellectual ability.(D) If proper measures are not taken, the decline in the student's academic performance may become irreversible.(E) Fluctuations in academic performance are typical for many students.

Young female ballet dancers and gymnasts sometimes fail to maintain good eating habits caused by the desire to be as thin as possible.

(A) Young female ballet dancers and gymnasts sometimes fail to maintain good eating habits caused by the desire to be as thin as possible.(B) Good eating habits sometimes fail to be maintained by young female ballet dancers and gymnasts caused by desiring to be as thin as possible.(C) Because they desire to be as thin as possible, good eating habits are sometimes not maintained by young female ballet dancers and gymnasts.(D) Because they desire to be as thin as possible, young female ballet dancers and gymnasts sometimes fail to maintain good eating habits.(E) Young female dancers and gymnasts sometimes fail to maintain good eating habits because they desire to be as thin as possible.

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