Jun 13, 2008

Kellogg

MBA, part-time, Kellogg

MBA, part-time, Kellogg (ZT)


I'm currently a part-time student in Kellogg and just finished my recruiting
this year, and have some inputs that you guys may find helpful about MBA,
part time, job hunting and Kellogg.

There are couple things important in b-school: the knowledge you learn, the
people you interact with, the career opportunities you have, and the brand
and alumni network you carry on (through your whole life).

I would put the knowledge you learn as the most important thing because in
the short term, it benefits your career search, A LOT (especially for career
changers); in the long term, it benefits your life-long career, simply
because pragmatism is dominant in b-schools – they only teach you practical
stuff. When measuring how much you learned in the school, GPA is
relatively the best tool (there are some exceptions, of course). During the
recruiting, a higher GPA can definitely give you an edge getting an
interview, especially for consulting (BCG, couple years before, only invite
students with higher than 3.75 GPA for close list interviews in Kellogg; on
the other hand, all the consulting firms require you to put GPA and GMAT
scores on application forms – they won’t require that if scores are not
important to them). Once you get the interview, the importance of scores
reduces – whether or not you can receive an offer is 90% based on your
performance during the interview. However, you won’t have an excellent
performance if you didn’t learn well during your previous classes – for
career changers, things you learned in b-school is the single most important
thing you can leverage to convince the interviewer that you can succeed in
the new industry (consulting, I-Banking, or etc.) All that being said, GPA
IS important, especially for career changers who have less experience.
Many people claim that networking is the key in b-schools. To some extent,
it is true; but others, it’s just exaggerated. The majority of your b-
school networking happens between you and your fellow students as well as
the professors. It’s them who give you the most valuable experience that
could benefit your academic achievement, job hunting, future career and even
how to be a better person. That being said, a top school with the culture
you fit well is extremely important: a top school is where all the smart
guys are, and many of them have great personalities, too; as for the culture
, it’s something hard to describe – you need to involve yourself in to
feel it (my feeling with Kellogg is that it’s indeed a supportive and
collegiate environment. Although sometimes teamwork is over-emphasized, it
does cultivate the “Kellogg Way”. Other schools may have culture that fit
you better – you need to find it yourself).

Contrary to many thoughts, networking does not mean being social with other
students – networking without common interests is ineffective and sometimes
just waste of time. Where can you find common interests? The easiest way
is to work together on the course projects and to prepare together for
interviews (such as case prep) – you can easily develop friendship with
your peers through the process. Of course if you are a very social person,
you can find more channels to develop the network. But if you happen to be
a “quiet guy”, developing your network just through regular student life
is also fine.

In the case of networking outside the student and faculty body, one
assumption has to be made: the purpose of your networking is to explore
career opportunities (for other purposes, such as to find your significant
other, I have no idea). The school and student clubs generate 90% of the
networking opportunities for you – in most cases, you will be already
overwhelmed, both time wise and energy wise. For certain kind of career,
such as I-Banking, network is critically important; while for others, such
as consulting, networking is much less the key.

When comparing networking opportunities for full time and part time students
, I would say “equal with some exceptions”, at least in Kellogg: majority
of the networking opportunities open to full time are also open to part
time; on the contrary, part time program create a lot of networking
opportunities that very few full time students come to attend. One
exception is the internship-related networking, which part time students do
not attend in a formal way. We will cover this later.

Career opportunity is the thing every MBA student cares much about –
otherwise, you won’t get into the program at the first place. There are
three major job categories for MBA students: Consulting, I-Banking and
corporate. To be honest, the career opportunities for full-time and part-
time are different – overall, career changers have better chances in a full
-time program; part-time students need to be more spontaneous to overcome
the gap. The difference is most obvious for I-Banking jobs, less for
consulting, and even less for corporate.

I-Banking is the hardest to break into if you do not have previous working
experience in finance or consulting, which is the target profile for banking
employers. That means, for career changers, if you do not have banking
intern, you have much less chance (on the other hand, if you do have a
banking intern, a full-time offer is almost guaranteed) – part-time
students usually do not have intern opportunities. For full-time career
changers, they face the same situation when interviewing for banking
internships. What they do is they will land a consulting intern first, and
then try to land a full-time banking one year later – the odds increase a
lot. Kellogg is not traditionally a banking school – for the past couple
years, there are usually around 5 part-time students successfully made the
career changes to banking, out of about 10 students who made the serious
attempts – so the odds is not that bad. However, those five are really
serious and spontaneous – some of them quitted the job to do an intern
first, and some others made a private trip to NYC to meet 40+ bankers in 10
days (you really need to be a “self-started networking guy” to do this).

Kellogg is more a consulting school – it has a super strong reputation
among all consulting firms – each year, around 1/3 of the class joins the
consulting industry, including internal consulting for corporate. Among the
200-ish offerees, about 100 accept the offers from the big 3: McKinsey, BCG
and Bain. There are also many other top strategy consulting firms, such as
Booz, Monitor, Marakon and ATK – they usually hire much less people.
Comparing consulting opportunities for full-time and part-time, the gap is
nominal. Part-time students may not be able to get as much close-list
invitations (by network + resume) as full-time fellows, but can make up
through open-list (by bidding). Overall, each consulting-focused student
can get at least 7-8 consulting interviews. Once you get into the interview
, firms care much less on your experience, networking or GPA (they still
affect their decisions though), but primarily on your performance in the
case-crack and fit. While in banking interviews, an excellent performance
in interview is not adequate to convince the firms – you need to do very
well in the networking or have a strong background (profile fit or intern)
to supplement the interview. Comparing to the case portion, the fit portion
is less decisive as long as you prepared for the basic questions (still a
lot) and did find some chemistry between yourself and the interviewer.

Corporate opportunities are equal in both programs, and may even favor part-
time students in some cases. Leadership and rotational programs prefer full
-time students because they are usually younger (it’s not a joke), while
functional positions (such as marketing, finance, or product management)
have more chances for part-time students because they just have more
experience. However, for the latter category, your background plays the key
– career changers have little chances for those positions – you better
compete with those “young faces” in the leadership programs.

There are also many other career opportunities: VC/PE, Asset Management, Non
-Profit, Entrepreneur and etc. They are not common categories and have much
higher requirements on previous experience and are more case-by-case.

In summary, the career opportunities for both programs in Kellogg do have
some difference but not much – everyone can get almost as much interviews
as he/she wants during the recruiting. However, the job placement for full-
time is better in average than for part-time. Here are the reasons, in my
opinion:

1.In recruiting, part-time students are not as committed as full-time (
because part-time have more back-up – they already have a job)
2.Part-time students are less flexible in job function/location – they
usually tend to have a family to raise, a mortgage to pay, a life-style to
keep or a green card to wait for 
3.The intellectual caliber of part-time is averagely a little bit lower than
that of full-time (it is sad to say that, but it is true. A simple example
, the GMAT score for Kellogg full time is 710 on average, and 690 for part-
time)
4.Part-time students are averagely older than full-time, and some industry
prefers younger candidates, such as I-Bnaking and leadership programs.

But when it comes to individual, this should not be your major concern when
choosing which program to apply for: you should be committed if you are
serious about changing your career, even in a full time program; you could
be more flexible if you are willing to give up something (excluding family,
of course); getting into a full-time program or a part-time does NOT affect
your intellectual caliber – on the contrary, you are contributing yours
into the program; you could act earlier to apply for the program, so that
your age will be below average.

Then what should we concern when deciding which program to choose?
Again, we will cover that later ...

May 21, 2008

GMATPREP SC (2x)

21. Shipwrecks are more likely to be found undisturbed at great depths than in shallow costal waters, which exposes archaeological remains to turbulence and makes them accessible to anyone in scuba gear, whether they be archaeologist, treasure hunter, or sport diver.

A. than in shallow costal waters, which exposes archaeological remains to turbulence and makes them accessible to anyone in scuba gear, whether they be

B. than in shallow costal waters, where archaeological remains are exposed to turbulence and are accessible to anyone in scuba gear, whether

C. as opposed to shallow waters along the coast, where archaeological remains are exposed to turbulence and accessible to anyone in scuba gear, including

D. instead of in shallow waters along the coast, which exposes archaeological remains to turbulence and making them accessible to anyone in scuba gear, including an

E. instead of shallow coastal waters, because it exposes archaeological remains to turbulence and make them accessible to anyone in scuba gear, whether

A: which refers to the subject of previous clause: incorrect; they can be removed.

B: Correct

C, D and E: more X should be followed by Than Y

22. As the former chair of the planning board for 18 consecutive years and a board member for 28 years, Joan Philkill attended more than 400 meetings and reviewed more than 700 rezoning applications.

A. As the former

B. The former

C. Former

D. She was

E. As the

A: the former chair and 18 consecutive years mean a repeat, wordy
B: Run on
C: Article “the’ missing
D: run on
E: correct

23. Unlike most severance packages, which require workers to stay until the last day scheduled to collect, workers at the automobile company are eligible for its severance package even if they find a new job before they are terminated.

A. the last day scheduled to collect, workers at the automobile company are eligible for its severance package

B. the last day they are scheduled to collect, workers are eligible for the automobile company's severance package

C. their last scheduled day to collect, the automobile company offers its severance package to workers

D. their last scheduled day in order to collect, the automobile company's severance package is available to workers

E. the last day that they are scheduled to collect, the automobile company's severance package is available to workers

A, B and C: wrong comparison, comparing severance package with worker.

D: Correct

There’s a subtle difference between D and E .

D. their last scheduled day in order to collect, the automobile company’s severance package is available to workers.
"their last scheduled day" means "their last working day". This doesn't imply that the workers will get the package on the last day but if they come on their last working day then they will get the package (may be some other day).

E. the last day that they are scheduled to collect, the automobile company’s severance package is available to workers.
"the last day that they are scheduled to collect" means the last day of "the days during which the packages can be collected". This doesn't have to be work day.

24. An international group of more than 2,000 scientists project an average global warming that will be between 1.8 and 6.3 degrees Fahrenheit by the year 2000.

A. project an average global warming that will be between 1.8 and

B. project an average global warming to be from 1.8 to

C. project global warming that will average between 1.8 and

D. projects global warming to average from 1.8 to

E. projects an average global warming of between 1.8 and

A, B and C: the verb should be singular: projects

D: average is placed wrongly

E: Correct

25. Ozone reaches high concentrations twelve miles above Earth, where it has long appeared that it was immune from human influence; we have now realized, though, that emissions of industrial chlorofluorocarbons deplete the ozone layer.

A) has long appeared that it was immune from

B) has long appeared to have been immune from

C) has long appeared as being immune to

D) had long appeared immune to

E) had long appeared that it was immune to

A, B, C and E: appear to, appear that, appear as being is incorrect usage. Appear / Appears X is correct.

D: correct

26. The electronics company has unveiled what it claims to be the world’s smallest network digital camcorder, the length of which is that of a handheld computer, and it weighs less than 11 ounces.

A. to be the world’s smallest network digital camcorder, the length of which is that of a handheld computer, and it weighs

B. to be the smallest network digital camcorder in the world, which is as long as a handheld computer, weighing

C.is the smallest network digital camcorder in the world, which is as long as a handheld computer, and it weighs

D.is the world’s smallest network digital camcorder, which is as long as a handheld computer and weighs

E.is the world’s smallest network digital camcorder, the length of which is that of a handheld computer, weighing

A. The clause after unveiled has no predicate. It has unclear reference.

B. weighing modifies computer or company?-

C: Which refers to world

D:CORRECT

E. Weighing modifies computer or company?

Note: claim +to+verb Vs claim +that=pretend, profess

She claimed that the ring was stolen, not lost.

She claims to be a good pianist.

29. There are hopeful signs that we are shifting away from our heavy reliance on fossil fuels: more than ten times as much energy is generated through wind power now than it was in 1990.

A) generated through wind power now than it was

B) generated through wind power now as it was

C) generated through wind power now as was the case

D) now generated through wind power as it was

E) now generated through wind power than was the case

“As Much As” is Idiom so A & E are out.

In 'B' and 'D ' there is no clear referent of 'it' refer to?.

C is the answer.

30. The Sports Medicine Programs of the Olympic Training Center, a complex where final try outs are held for athletes representing the US in the Olympics, is geared toward enhancing athletes' performance and toward their preparation for international competition.

A.) is geared toward enhancing athletes' performance and toward their preparation

B.) is geared to enhance the performance of athletes and to prepare them
C.) are geared to enhance athletes performance and their preparation
D.) are geared toward the enhancement of athletes' performance and toward preparing them

E.) are geared toward enhancing the performance of athletes and preparing them

A: is to be plural, not toward the back parallel
B: is the plural should be changed
C: enhance their preparation illogical
D: parallel and inconsistency
E: correct

Monday, March 10, 2008

GMAT PREP SC 11-20

11. Before scientists learned how to make a synthetic growth hormone, removing it painstakingly in small amounts from the pituitary glands of human cadavers.

A. scientists learned how to make a synthetic growth hormone, removing it painstakingly

B. scientists had learned about making a synthetic growth hormone, they had to remove it painstakingly

C. scientist learned how to synthesize the growth hormone, it had to be painstakingly removed

D. learning how to make a synthetic growth hormone, scientists had to remove it painstakingly

E. Learning how to synthesize the growth hormone, it have to be painstakingly removed by scientists

A: the main clause relationship is not established; the sentence is incomplete.

B: the antecedent of it is not clear

C: correct

D: it no clear antecedent

E: it and have mismatch

12. The success of the program to eradicate smallpox has stimulated experts to
pursue what they had not previously considered possible -- better control, if not eradication, of the other infections such as measles and yaws.

A. what they had not previously considered possible -- better control, if not eradication, of the other infections such as

B. what they had not previously considered a possibility -- better control, if not eradication, of such infections like

C. something they had not previously considered possible -- better control, if not eradication, of such infections as

D. something not considered a previous possibility -- better control and perhaps eradication, of other infections such as

E. the possibility of what they had not previously considered possible – better control and possibly eradication of infections like

A: Unusual break with semi colon

B: use of Such……like

C: correct

D: previous is not required, possibility is good enough. Perhaps not required.

E: wordy

13. A study of food resources in the North Pacific between 1989 and 1996 revealed that creatures of the seabed were suffering from dwindling food supplies, possibly resulting from increasing sea surface temperatures during the same period.

a) that creatures of the seabed were suffering from dwindling food supplies, possibly resulting from increasing

b) that creatures of the seabed were suffering because food supplies were dwindling, possibly as a result of an increase in

c) that creatures of the seabed were suffering because of food supplies, which were dwindling possibly as a result of increasing

d) creatures of the seabed that were suffering from food supplies that were dwindling, possibly resulting from an increase in

e) creatures of the seabed that were suffering because food supplies were dwindling, which possibly resulted from increasing

A: the ing form is incorrect ( increasing)

B: correct

C: “because of food supplies” is a less succinct expression; the ing form is incorrect ( increasing)

D: studies revealed creature…. Changes meaning

E: studies revealed creature…. Changes meaning

14. The largest trade-book publisher in the US has announced the creation of a new digital imprint division, under which it will publish about 20 purely digital works to be sold online as either electronic books or downloadable copies that can be printed upon purchase.

A) works to be sold online as either electronic books or
B) works to sell them online, either as electronic books or
C) works and it will sell them online as either electronic books or as
D) works, and selling them online as either electronic books or as
E) works, and it will sell them online as either electronic books or

A: Correct; Correct form a) either as X or as Y or B) as either A or B

B: wrong structure

C: and it will is wordy; wrong structure for either

D: creation is not parallel with selling; either wrong structure

E: either wrong structure; wordy

15. Recently documented examples of neurogenesis, the production of new brain cells, include the brain growing in mice when placed in a stimulating environment or neurons increasing in canaries that learn new songs.

A. the brain growing in mice when placed in a stimulating environment or neurons increasing in canaries that

B. mice whose brains grow when they are placed in a stimulating environment or canaries whose neurons increase when they

C. mice's brains that grow when they are placed in a stimulating environment or canaries' neurons that increase when they

D. the brain growth in mice when placed in a stimulating environment or the increase in canaries' neurons when they

E. brain growth in mice that are placed in a stimulating environment or an increase in neurons in canaries that

A: growing should be replaced by growth; increasing by increase; also sentence suggests that brain growing is placed in stimulating environment.

B: antecedent of they is unclear

C: Logically incorrect, suggest brains are put in environment

D: suggest brain growth is placed in environment

E: correct

16. Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil, their descendents, popularly known as killer bees had migrated as far north as Southern Texas.

A. Less than 35 years after the release of African honeybees outside Sao Paulo, Brazil,

B. In less than 35 years since releasing African honeybees outside Sao Paulo, Brazil,

C. In less than the 35 years since African honeybees had been released outside Sao Paulo, Brazil,

D. It took less than 35 years from the release of African honeybees outside Sao Paulo, Brazil, when

E. It took less than 35 years after the time that African honeybees were released outside Sao Paulo, Brazil, and then

A: correct

B and C: in less than 35 year talks about future rather than past

D: it took less than 35 years and when doesn’t match; when indicates exact time frame

E: their should refer to subject of previous clause which is it. Mismatch

17. The new image of Stone Age people as systematic hunters of large animals, rather than merely scavenging for meat, have emerged from the examination of tools found in Germany, including there wooden spears that archaeologists believe to be about 400,000 years old.

A. merely scavenging for meat, have emerged from the examination of tools found in Germany, including

C. as mere meat scavengers, has emerged from examining tools found in Germany that includes

D. mere scavengers of meat, has emerged from the examination of tools found in Germany, which includes

E. mere scavengers of meat, has emerged from the examination of tools found in Germany, including

I feel all the options are wrong here, however OA is E. Please comment

18. There is a widespread belief in the US and Western Europe that young people have a smaller commitment to work and a career than their parents and grandparents and that the source of the change lies in the collapse of the 'work ethic'.

A. a smaller commitment to work and a career than their parents and grandparents

B. less of a commitment to work and a career than their parents and grandparents

C. a smaller commitment to work and a career than their parents and grandparents

D. less of a commitment to work and a career than their parents and grandparents had

E. a lessening of the commitment to work and a career than their parents and grandparents had

A B C : comparing commitment to parents and grand parents

D correct

E: wordy; ” lessening of change “ should be less of,” gerund form

19. Industrialization and modern methods of insect control have improved the standard of living around the globe while at the same time they have introduced some 100,000 dangerous chemical pollutants, having gone virtually unregulated since they were developed more than 50 years ago.

A. while at the same time they have introduced some 100,000 dangerous chemical pollutants, having

B. while at the same time introducing some 100,000 dangerous chemical pollutants that have

C. while they have introduced some 100,000 dangerous chemical pollutants at the same time, which have

D. but introducing some 100,000 dangerous chemical pollutants at the same time that have

E. but at the same time introducing some 100,000 dangerous chemical pollutants, having

A and C: “they “has no antecedent

B: correct

D: introducing is not parallel with have improved

E: incomplete sentence

20. An international team of astronomers working at telescopes in the Canary Islands and Spain has detected at least 18 huge gas spheres estimated to have 5 to 15 times the mass of Jupiter, the solar system’s largest planet.

A.) astronomers working at telescopes in the Canary Islands and Spain has detected at least 18 huge gas spheres estimated to have 5 to 15 times the mass of Jupiter

B.) astronomers working at telescopes in the Canary Islands and Spain has detected at least 18 huge gas spheres estimated to be 5 to 15 times Jupiter’s mass

C.) astronomers is working at telescopes in the Canary Islands and Spain, having detected at least 18 huge gas sphere that are estimated at 5 to 15 times the mass of Jupiter

D.) astronomers, working at telescopes in the Canary Islands and Spain, and has detected at least 18 huge gas spheres estimated at 5 to 15 times the mass of Jupiter

E.) astronomers, working at telescopes in the Canary Islands and Spain, has detected at least 18 huge gas spheres they have estimated to be 5 to 15 times Jupiter’s mass

A: Correct

B: Jupiter’s mass cannot be the solar system’s largest planet

C: estimated at ?? , having detected and is working is not parallel

D: the first clause has only subject. After removing the modifier, the sentence effectively reduces to : An international team of astronomers and has detected huge gas…….

E: Run-on

Sunday, March 9, 2008

GMAT PREP SC 1-10

1. The Anasazi settlements at Chaco Canyon were built on a spectacular scale with more than 75 carefully engineered structures, of up to 600 rooms each, were connected by a complex regional system of roads.
A. with more than 75 carefully engineered structures, of up to 600 rooms each, were
B. with more than 75 carefully engineered structures, of up to 600 rooms each,
C. of more than 75 carefully engineered structures of up to 600 rooms, each that had been
D. of more than 75 carefully engineered structures of up to 600 rooms and with each
E. of more than 75 carefully engineered structures of up to 600 rooms each had been

A: Predicate were repeated, it should be removed
B: correct, the word modified sentence connected Subject settlements
C: Modified Structures of the second wrong, it should be modified scale; each clause with the language used in the past when there was no need to complete,
D: The second modification of Structures wrong, it should be modified scale; and with each no parallel objects,
E: Modified Structures of the second wrong, it should be modified scale; behind each is a complete sentence but did not Conjunction

NOTE:
1, The Anasazi settlements at Chaco Canyon were built on a spectacular scale of up to 600 rooms each, connected by a complex regional system of roads. Each refers to The Anasazi settlements, rather than rooms or structures!
2, the modified objects preposition, Parenthesis, comma + past participle, and the use of modified objects

2. According to one expert, the cause of genetic irregularities in many breeds of dog is not so much that dogs are being bred for looks or to meet other narrow criteria as that the breeds have relatively few founding members.
A. the cause of genetic irregularities in many breeds of dog is not so much that dogs are being bred for looks or to meet other narrow criteria
B. the cause of genetic irregularities in many breeds of dog is not as much their being bred for looks or meeting other narrow criteria as much
C. it is not so much the cause of genetic irregularities in many breeds of dog that they are being bred for looks or meeting other narrow criteria as much
D. it is not so much the cause of genetic irregularities in many breeds of dog is their being bred for looks or meeting other narrow criteria so much
E. it is not so much the cause of genetic irregularities in many breeds of dog to be bred for looks or to meet other narrow criteria

A: correct, for looks or to meet parallel modified predicate bred
B: not so much their… as much as that is not parallel
C: Biaoyu clause use it wrong, not so as… as much as non-parallel
D: Ditto, and the second is redundant, not so much… so much as the wrong usage
E: Ditto, to be bred to meet and not parallel logic

NOTE:
1, not so much that… as that… more than that, in parallel form
2, for looks or to meet the functional form parallel rather than in parallel, said that the purpose be bred
3, the surface, the E to be done and to do the parallel form, but the logic is wrong modified object is confusing options.

3. Greatly influenced by the Protested missionary Samuel Kirkland, the Oneida was the only one of the five-nation Iroquois League who sided with the colonists during the American Revolution.
A. was the only one of the five-nation Iroquois League who sided
B. was alone of the five-nation Iroquois League when they sided
C. alone among the five-nation Iroquois League sided
D. were the only ones out of the five nations of Iroquois League in siding
E. only of the five-nation Iroquois League had sided

A: was should be "were" ; one of the many nation that sided...
B: was should be were
C: correct, the Oneida… sided with ... alone among the five-nation Iroquois League qualifier is modified Oneida
D: the only ones should be replaced by the only one
E: modified structure errors, not only of use, should be used during the past sometimes the past is not complete




4. Although the turtle has been toothless for more than 150 million years, in some contemporary turtle species the moderately sharp and jagged edges of their horny jaws function for teeth.
A. their horny jaws function for teeth
B. its horny jaws function for teeth
C. its horny jaws function as do teeth
D the horny jaws function as teeth do
E the horny jaws function as teeth

A: Use a fixed function as n.
B: its refers to the wrong species should be
C:
D: function as n. fixed usage, not here as compared to guide sentence
E: correct

NOTE: function as… and A do as B do the logical meaning of distinction
Distinguish between A do as B do and some as with the difference between the fixed


5. The Achaemenid empire of Persia reached the Indus Valley in the fifth century BC, bringing the Aramaic script with it, from which was derived both northern and southern India alphabets.
A. the Aramaic script with it, from which was derived both northern and
B. the Aramaic script with it, and from which deriving both the northern and the
C. with it the Aramaic script, from which derive both the northern and the
D. with it the Aramaic script, from which derives both northern and
E. with it the Aramaic script, and deriving from it both the northern and

A: from which the generation which means it wrong, was to use were
B: and wrong, no need for parallel
C: correct, the second part is the flip should be both the northern and the southern India alphabets derive from the Aramaic script
D: derives in the plural
E: and does not need a comma before, and also bringing with deriving should not be a subject




6. In the past several years, astronomers have detected more than 80 massive planets, most of them as large or larger than Jupiter, which circle other stars.
A. most of them as large or larger than Jupiter, which circle
B. most of them as large or larger than Jupiter and circling
C. most of them at least as large as Jupiter, circling
D. mostly at least as large as Jupiter, which circle
E. mostly as large or larger than Jupiter, circling

A: as large or larger than incomplete, it should be added as
B: Ditto, and circling no parallel in front of the elements
C: correct, circling modified planets, but there is a degree of ambiguity modified Jupiter
D: mostly mean wrong, can be modified at least not planets; which circle modified planets is right
E:


7. Each year companies in the United State could save as much as $ 58 billion annually by preventing illness among employees and gain as much as $ 200 billion through improving performance of workers if they simply provided offices with cleaner air.

A. annually by preventing illness among employees and gain as much as $ 200 billion through improving performance of workers if they simply provided
B. annually if they prevented employee illness and gain as much as $ 200 billion through worker performance improved by simply providing
C. annually in employee illness prevention and gain as much as $ 200 billion through worker performance improved by simply providing
D. in employee illness prevention and gain as much as $ 200 billion through improving performance of workers if they simply provided
E. by preventing illness among employees and gain as much as $ 200 billion through improved worker performance if they simply provided

A: each year and annually mean duplication, improving the process did not table a result, improved application,
B:
C:
D: in employee illness prevention to express the meaning wrong,
E: correct

8. Women are expected to be the majority of student entering law school this fall, a trend ultimately placing more women in leadership position in politics and business.
A Women are expected to be the majority of student entering law school this fall, a trend ultimately placing
B The majority of students entering law school this fall are expected to be women, a trend that will ultimately place
C The majority of students entering law school this fall are expected to be women, which will ultimately place
D It is expected that the majority of students entering law school this fall will be women, a trend ultimately placing
E It is expected for the women to be the majority of students entering law school this fall, which will ultimately place

A: placing the same language in the structure can not be shown to be the trend, but has happened
B: correct use that phrase clause modified trend clearly indicates that the action to take place
C: which means no generation
D: same as A
E: same as C


9. The investigations of many psychologist and anthropologists support the generalization of there being little that is a significant difference in underlying mental processes manifested by people from different culture.
A of there being little that is a significant difference
B of there being little that is significantly different
C of little that is significantly different
D that there is little that is significantly different
E that there is little of significant differences

A: of there being wrong.
B:
C: ditto
D: correct, the term is little, that little clause modified
E: little of the general increase uncountable noun, meaning at the same time deny expression

10. The yield per acre of coffee berries varies enormously in that a single tree, depending on both its size and on climate and altitude, could produce enough berries to make between one and twelve pounds of dried beans a year.

A. enormously in that a single tree, depending on both its size and on climate and altitude, could produce

B. enormously in that a single tree, dependent on its size and also on climate and altitude, is able to produce

C. enormously, because a single tree, depending on its size and on climate and altitude, is able to produce

D. enormously, because a single tree, being dependent on its size, climate, and altitude, and is capable of producing

E. enormously, because a single tree, dependent both on its size as well as on climate and altitude, could produce

A: both on X and on Y is parallel.

B: dependent vs depending, because is more preferable here

C: correct

D: being dependent …incorrect

E: structure of both not parallel

May 2, 2008

Math: Combination vs. Permutation - Circular-permutations

Circular permutations

There are two cases of circular-permutations:-

(a) If clockwise and anti clock-wise orders are different, then total number of circular-permutations is given by (n-1)!

(b) If clock-wise and anti-clock-wise orders are taken as not different, then total number of circular-permutations is given by (n-1)!/2!

Proof(a):

(a) Let’s consider that 4 persons A,B,C, and D are sitting around a round table

Shifting A, B, C, D, one position in anticlock-wise direction, we get the following agreements:-


Thus, we use that if 4 persons are sitting at a round table, then they can be shifted four times, but these four arrangements will be the same, because the sequence of A, B, C, D, is same. But if A, B, C, D, are sitting in a row, and they are shifted, then the four linear-arrangement will be different.

Hence if we have ‘4’ things, then for each circular-arrangement number of linear-arrangements =4

Similarly, if we have ‘n’ things, then for each circular – agreement, number of linear – arrangement = n.

Let the total circular arrangement = p

Total number of linear–arrangements = n.p

Total number of linear–arrangements

= n. (number of circular-arrangements)

Or Number of circular-arrangements = 1 (number of linear arrangements)

n = 1( n!)/n

circular permutation = (n-1)!

Proof (b) When clock-wise and anti-clock wise arrangements are not different, then observation can be made from both sides, and this will be the same. Here two permutations will be counted as one. So total permutations will be half, hence in this case.

Circular–permutations = (n-1)!/2

Note: Number of circular-permutations of ‘n’ different things taken ‘r’ at a time:-

(a) If clock-wise and anti-clockwise orders are taken as different, then total number of circular-permutations = nPr /r

(b) If clock-wise and anti-clockwise orders are taken as not different, then total number of circular – permutation = nPr/2r

Example: How many necklace of 12 beads each can be made from 18 beads of different colours?

Ans. Here clock-wise and anti-clockwise arrangement s are same.

Hence total number of circular–permutations: 18P12/2x12

= 18!/(6 x 24)

Restricted – Permutations

(a) Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is to be always included in each arrangement

= r n-1 Pr-1

(b) Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is fixed: = n-1 Pr-1

(c) Number of permutations of ‘n’ things, taken ‘r’ at a time, when a particular thing is never taken: = n-1 Pr.

(d) Number of permutations of ‘n’ things, taken ‘r’ at a time, when ‘m’ specified things always come together = m! x ( n-m+1) !

(e) Number of permutations of ‘n’ things, taken all at a time, when ‘m’ specified things always come together = n ! - [ m! x (n-m+1)! ]

Example: How many words can be formed with the letters of the word ‘OMEGA’ when:

(i) ‘O’ and ‘A’ occupying end places.

(ii) ‘E’ being always in the middle

(iii) Vowels occupying odd-places

(iv) Vowels being never together.

Ans.

(i) When ‘O’ and ‘A’ occupying end-places

=> M.E.G. (OA)

Here (OA) are fixed, hence M, E, G can be arranged in 3! ways

But (O,A) can be arranged themselves is 2! ways.

=> Total number of words = 3! x 2! = 12 ways.

(ii) When ‘E’ is fixed in the middle

=> O.M.(E), G.A.

Hence four-letter O.M.G.A. can be arranged in 4! i.e 24 ways.

(iii) Three vowels (O,E,A,) can be arranged in the odd-places (1st, 3rd and 5th) = 3! ways.

And two consonants (M,G,) can be arranged in the even-place (2nd, 4th) = 2 ! ways

=> Total number of ways= 3! x 2! = 12 ways.

(iv) Total number of words = 5! = 120!

If all the vowels come together, then we have: (O.E.A.), M,G

These can be arranged in 3! ways.

But (O,E.A.) can be arranged themselves in 3! ways.

=> Number of ways, when vowels come-together = 3! x 3!

= 36 ways

=> Number of ways, when vowels being never-together

= 120-36 = 84 ways.

Number of Combination of ‘n’ different things, taken ‘r’ at a time is given by:-

nCr= n! / r ! x (n-r)!

Proof: Each combination consists of ‘r’ different things, which can be arranged among themselves in r! ways.

=> For one combination of ‘r’ different things, number of arrangements = r!

For nCr combination number of arrangements: r nCr

=> Total number of permutations = r! nCr ---------------(1)

But number of permutation of ‘n’ different things, taken ‘r’ at a time

= nPr -------(2)

From (1) and (2) :

nPr = r! . nCr

or n!/(n-r)! = r! . nCr

or nCr = n!/r!x(n-r)!

Note: nCr = nCn-r

or nCr = n!/r!x(n-r)! and nCn-r = n!/(n-r)!x(n-(n-r))!

= n!/(n-r)!xr!

Restricted – Combinations

(a) Number of combinations of ‘n’ different things taken ‘r’ at a time, when ‘p’ particular things are always included = n-pCr-p.

(b) Number of combination of ‘n’ different things, taken ‘r’ at a time, when ‘p’ particular things are always to be excluded = n-pCr

Example: In how many ways can a cricket-eleven be chosen out of 15 players? if

(i) A particular player is always chosen,

(ii) A particular is never chosen.

Ans:

(i) A particular player is always chosen, it means that 10 players are selected out of the remaining 14 players.

=. Required number of ways = 14C10 = 14C4

= 14!/4!x19! = 1365

(ii) A particular players is never chosen, it means that 11 players are selected out of 14 players.

=> Required number of ways = 14C11

= 14!/11!x3! = 364

(iii) Number of ways of selecting zero or more things from ‘n’ different things is given by:- 2n-1

Proof: Number of ways of selecting one thing, out of n-things = nC1

Number of selecting two things, out of n-things =nC2

Number of ways of selecting three things, out of n-things =nC3

Number of ways of selecting ‘n’ things out of ‘n’ things = nCn

=>Total number of ways of selecting one or more things out of n different things

= nC1 + nC2 + nC3 + ------------- + nCn

= (nC0 + nC1 + -----------------nCn) - nC0

= 2n – 1 [ nC0=1]

Example: John has 8 friends. In how many ways can he invite one or more of them to dinner?

Ans. John can select one or more than one of his 8 friends.

=> Required number of ways = 28 – 1= 255.

(iv) Number of ways of selecting zero or more things from ‘n’ identical things is given by :- n+1

Example: In how many ways, can zero or more letters be selected form the letters AAAAA?

Ans. Number of ways of :

Selecting zero 'A's = 1

Selecting one 'A's = 1

Selecting two 'A's = 1

Selecting three 'A's = 1

Selecting four 'A's = 1

Selecting five 'A's = 1

=> Required number of ways = 6 [5+1]

(V) Number of ways of selecting one or more things from ‘p’ identical things of one type ‘q’ identical things of another type, ‘r’ identical things of the third type and ‘n’ different things is given by :-

(p+1) (q+1) (r+1)2n – 1

Example: Find the number of different choices that can be made from 3 apples, 4 bananas and 5 mangoes, if at least one fruit is to be chosen.

Ans:

Number of ways of selecting apples = (3+1) = 4 ways.

Number of ways of selecting bananas = (4+1) = 5 ways.

Number of ways of selecting mangoes = (5+1) = 6 ways.

Total number of ways of selecting fruits = 4 x 5 x 6

But this includes, when no fruits i.e. zero fruits is selected

=> Number of ways of selecting at least one fruit = (4x5x6) -1 = 119

Note :- There was no fruit of a different type, hence here n=o

=> 2n = 20=1

(VI) Number of ways of selecting ‘r’ things from ‘n’ identical things is ‘1’.

Example: In how many ways 5 balls can be selected from ‘12’ identical red balls?

Ans. The balls are identical, total number of ways of selecting 5 balls = 1.

Example: How many numbers of four digits can be formed with digits 1, 2, 3, 4 and 5?

Ans. Here n = 5 [Number of digits]

And r = 4 [ Number of places to be filled-up]

Required number is 5P4 = 5!/1! = 5 x 4 x 3 x 2 x 1

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