GMAT Problem Solving Discussions

oh! GMAT guru

aap humare yaha darshan dene kab aaoge

btw which r the posts # still unanswered? pls let me know since i hv PC to check it myself. πŸ˜ƒ

hey! we already hv a thread for CR right?

sorry i dont participate in any of the threads ...
but now i ll try.

pls let me know :thumbsup:

oh! GMAT guru

aap humare yaha darshan dene kab aaoge

btw which r the posts # still unanswered? pls let me know since i hv PC to check it myself. πŸ˜ƒ

hey! we already hv a thread for CR right?

sorry i dont participate in any of the threads ...
but now i ll try.

pls let me know :thumbsup:

Hi aim, in the other thread, normal problems were discussed. Here am posting the tough problems. There are some post which are not answered. Why dont you try? I will keep posting good porblems. This is not jsut CR thread, covers all problems related to GMAT. And am not posting the easy ones much, cos they will be there in other gmat threads.

hey buddy, πŸ˜ƒ

change the name of the thread then.
also i asked for the unanswered posts which you hv not provided me 😞

oops i forgot to add ''dont'' there & damn i connot edit my posts since i DONT hv a PC!
and thats why i requested for posts #.
hope now you got my point. πŸ˜ƒ
pls provide unanswered posts #

first of all I am no guru wuru!!
I love CR's !! I feel that the answer is D

I generally solve by assuming the answer to be true and then see what happens...if d happens....the whole pupose is defeated...cuz they are misusing the scheme...the retailers...accumulating will benefit the retailers as they will get guds at lower prices but the customers wont benefit from the scheme...the imp point to look for here is :
Such promotion often result in a dramatic increase in amount of product sold by the manufacturers to retailers.
manufacturer to retailer....not to customer!!!
all other choices are out of scope...competitors, new products, consumer products are misleading...and shift of scope...u r adding adjetives here...not allowed when u hav to argue.
that eliminates B, C and E
A is infact counter evidence....cuz it says that the scheme will help the manufacturers...but see carefully...here we hav to prove that the scheme is not wise!!

Tip: eliminate first. Also see what we have to prove disprove...
I am not comfy with thinkin in english....i translate the whole thing into simple hindi in my mind and then i can relate it much more logically in my mind....works for me...doesnt mean english is poor...jus that the brain works better in ur native environ...

so i translated it into somethin like....
isse fayada hoga kya?? :wow:

hope that helps!!

cool mucool... :)
Thnx for the lucid explanation.

cheers!
Satish

Hi Guys,

I read the problem just now and even I feel that the answer is D because, for me the crux of solving this problem lies in the last line "Nevertheless the manufacturers can increase their profit by not resorting to promotions".

If this is the contention then A, B, C and E are simply ruled out. D did not appeal to me as a sure shot answer but since the others are oposite of what is desired I will go with it.

Guys, I need your help I somehow can't push my accuracy in CR and RC over the 90% mark. I am lurking around the 80-85% mark and a weird pattern I noticed especially in RCs. The questions I ge wrong tend to get bunched up, meaning I will get 20-25 questions correct and suddenly 3-4 questions within a span of 10-13 questions wrong.

Am I doing a strategic mistake or is there only a concentration lapse which is causing the mistakes, and these mistakes are topic independent.

Help wanted,...........


Thanks

More questions to be answered, please attempt:

1. The country of Maravia has severe air pollution,
80 percent of which is caused by the exhaust fumes
of cars. In order to reduce the number of cars on the
road, the government is raising taxes on the cost of
buying and running a car by 20 percent. This tax
increase, therefore, will significantly reduce air pollu-
tion in Maravia.

Which of the following, if true, most seriously
weakens the argument above?
(A) The government of Maravia is in the process of
building a significant number of roadways.
(B) Maravia is an oil-producing country and is able
to refine an amount of gasoline sufficient for
the needs of its population.
(C) Maravia has had an excellent public transporta-
tion system for many years.
(D) Ninety percent of the population of Maravia is
very prosperous and has a substantial
amount of disposable income.
(E) In Maravia, cars that emit relatively low levels
of pollutants cost 10 percent less to operate,
on average, than do cars that emit high levels
of pollutants.

10. The geese that gather at the pond of a large corpora-
tion create a hazard for executives who use the
corporate helicopter, whose landing site is 40 feet
away from the pond. To solve the problem, the
corporation plans to import a large number of herd-
ing dogs to keep the geese away from the helicopter.

Which of the following, if a realistic possibility,
would cast the most serious doubt on the prospects
for success of the corporation's plan?
(A) The dogs will form an uncontrollable pack.
(B) The dogs will require training to learn to herd
the geese.
(C) The dogs will frighten away foxes that prey on
old and sick geese.
(D) It will be necessary to keep the dogs in quaran-
tine for 30 days after importing them.
(E) Some of the geese will move to the pond of
another corporation in order to avoid being
herded by the dogs.

13. Houses built during the last ten years have been
found to contain indoor air pollution at levels that
are, on average, much higher than the levels found
in older houses. The reason air-pollution levels are
higher in the newer houses is that many such houses
are built near the sites of old waste dumps or where
automobile emissions are heavy.

Which of the following, if true, calls into question
the explanation above?
(A) Many new houses are built with air-filtration
*systems that remove from the house pollu-
*tants that are generated indoors.
(B) The easing of standards for smokestack emis-
*sions has led to an increase in air-pollution
*levels in homes.
(C) New houses built in secluded rural areas are
*relatively free of air pollutants.
(D) Warm-weather conditions tend to slow down
*the movement of air, thus keeping pollution
*trapped near its source.
(E) Pressboard, an inexpensive new plywood substi-
*tute now often used in the construction of
*houses, emits the pollutant formaldehyde into
*the house.

16. In a study of the effect of color on productivity,
50 of 100 factory workers were moved from their
drab workroom to a brightly colored workroom.
Both these workers and the 50 who remained in the
drab workroom increased their productivity, proba-
bly as a result of the interest taken by researchers in
the work of both groups during the study.

Which of the following, if true, would cast most
doubt upon the author's interpretation of the study
results given above?
(A) The 50 workers moved to the brightly colored
*room performed precisely the same manufac-
*turing task as the workers who remained in
*the drab workroom.
(B) The drab workroom was designed to provide
*adequate space for at most 65 workers.
(C) The 50 workers who moved to the brightly
colored workroom were matched as closely
as possible in age and level of training to the
50 workers who remained in the drab work-room.
(D) Nearly all the workers in both groups had
*volunteered to move to the brightly colored
*workroom.
(E) Many of the workers who moved to the
*brightly colored workroom reported that
*they liked the drab workroom as well as or
*better than they liked the brightly colored
*workroom.

16. For a trade embargo against a particular country to
succeed, a high degree of both international accord
and ability to prevent goods from entering or leav-
ing that country must be sustained. A total blockade
of Patria's ports is necessary to an embargo, but
such an action would be likely to cause international
discord over the embargo.

The claims above, if true, most strongly support
which of the following conclusions?
(A) The balance of opinion is likely to favor Patria
*in the event of a blockade.
(B) As long as international opinion is unanimously
*against Patria, a trade embargo is likely to
*succeed.
(C) A naval blockade of Patria's ports would ensure
*that no goods enter or leave Patria.
(D) Any trade embargo against Patria would be
*likely to fail at some time.
(E) For a blockade of Patria's ports to be success-
*ful, international opinion must be unani-
mous.
9. Hotco oil burners, designed to be used in asphalt plants,
are so efficient that Hotco will sell one to the Clifton
Asphalt plant for no payment other than the cost
savings between the total amount the asphalt plant
actually paid for oil using its former burner during
the last two years and the total amount it will pay
for oil using the Hotco burner during the next two
years. On installation, the plant will make an esti-
mated payment, which will be adjusted after two
years to equal the actual cost savings.

Which of the following, if it occurred, would consti-
tute a disadvantage for Hotco of the plan described
above?

(A) Another manufacturer's introduction to the
*market of a similarly efficient burner
(B) The Clifton Asphalt plant's need for more than
*one new burner
(C) Very poor efficiency in the Clifton Asphalt
*plant's old burner
(D) A decrease in the demand for asphalt
(E) A steady increase in the price of oil beginning
*soon after the new burner is installed

Thanks..............

My take.....

1) The country of Maravia ...... => D
10) The geese that gather ...... => E
13) Houses built during the .... => E
16) In a study of the effect ... => A
9) Hotco oil burners, designed . => D

CR.....
PS: Post the analysis also.

American productivity is declining in relation to Europe's; the energy expended per unit of production in the United States is as much as twice that expended in West Germany.

(A) as much as twice that expended in West Germany
(B) as much as twice that of West Germany's expenditure
(C) up to two times of West Germany's expenditure
(D) up to two times what West Germans expended
(E) up to double the West German expenditure

More questions to be answered, please attempt:
1. The country of Maravia has severe air pollution,
80 percent of which is caused by the exhaust fumes
of cars. In order to reduce the number of cars on the
road, the government is raising taxes on the cost of
buying and running a car by 20 percent. This tax
increase, therefore, will significantly reduce air pollu-
tion in Maravia.
Which of the following, if true, most seriously
weakens the argument above?
(A) The government of Maravia is in the process of
building a significant number of roadways.
(B) Maravia is an oil-producing country and is able
to refine an amount of gasoline sufficient for
the needs of its population.
(C) Maravia has had an excellent public transporta-
tion system for many years.
(D) Ninety percent of the population of Maravia is
very prosperous and has a substantial
amount of disposable income.
(E) In Maravia, cars that emit relatively low levels
of pollutants cost 10 percent less to operate,
on average, than do cars that emit high levels
of pollutants.

I am sure many of my attempts are going to be wrong...but still here is my take:
Maravia ----> D


10. The geese that gather at the pond of a large corpora-
tion create a hazard for executives who use the
corporate helicopter, whose landing site is 40 feet
away from the pond. To solve the problem, the
corporation plans to import a large number of herd-
ing dogs to keep the geese away from the helicopter.
Which of the following, if a realistic possibility,
would cast the most serious doubt on the prospects
for success of the corporation's plan?
(A) The dogs will form an uncontrollable pack.
(B) The dogs will require training to learn to herd
the geese.
(C) The dogs will frighten away foxes that prey on
old and sick geese.
(D) It will be necessary to keep the dogs in quaran-
tine for 30 days after importing them.
(E) Some of the geese will move to the pond of
another corporation in order to avoid being
herded by the dogs.

geese---> A

13. Houses built during the last ten years have been
found to contain indoor air pollution at levels that
are, on average, much higher than the levels found
in older houses. The reason air-pollution levels are
higher in the newer houses is that many such houses
are built near the sites of old waste dumps or where
automobile emissions are heavy.
Which of the following, if true, calls into question
the explanation above?
(A) Many new houses are built with air-filtration
*systems that remove from the house pollu-
*tants that are generated indoors.
(B) The easing of standards for smokestack emis-
*sions has led to an increase in air-pollution
*levels in homes.
(C) New houses built in secluded rural areas are
*relatively free of air pollutants.
(D) Warm-weather conditions tend to slow down
*the movement of air, thus keeping pollution
*trapped near its source.
(E) Pressboard, an inexpensive new plywood substi-
*tute now often used in the construction of
*houses, emits the pollutant formaldehyde into
*the house.

Houses----> E


16. In a study of the effect of color on productivity,
50 of 100 factory workers were moved from their
drab workroom to a brightly colored workroom.
Both these workers and the 50 who remained in the
drab workroom increased their productivity, proba-
bly as a result of the interest taken by researchers in
the work of both groups during the study.
Which of the following, if true, would cast most
doubt upon the author's interpretation of the study
results given above?
(A) The 50 workers moved to the brightly colored
*room performed precisely the same manufac-
*turing task as the workers who remained in
*the drab workroom.
(B) The drab workroom was designed to provide
*adequate space for at most 65 workers.
(C) The 50 workers who moved to the brightly
colored workroom were matched as closely
as possible in age and level of training to the
50 workers who remained in the drab work-room.
(D) Nearly all the workers in both groups had
*volunteered to move to the brightly colored
*workroom.
(E) Many of the workers who moved to the
*brightly colored workroom reported that
*they liked the drab workroom as well as or
*better than they liked the brightly colored
*workroom.

workman----> B

16. For a trade embargo against a particular country to
succeed, a high degree of both international accord
and ability to prevent goods from entering or leav-
ing that country must be sustained. A total blockade
of Patria's ports is necessary to an embargo, but
such an action would be likely to cause international
discord over the embargo.
The claims above, if true, most strongly support
which of the following conclusions?
(A) The balance of opinion is likely to favor Patria
*in the event of a blockade.
(B) As long as international opinion is unanimously
*against Patria, a trade embargo is likely to
*succeed.
(C) A naval blockade of Patria's ports would ensure
*that no goods enter or leave Patria.
(D) Any trade embargo against Patria would be
*likely to fail at some time.
(E) For a blockade of Patria's ports to be success-
*ful, international opinion must be unani-
mous.

embargo----> E

9. Hotco oil burners, designed to be used in asphalt plants,
are so efficient that Hotco will sell one to the Clifton
Asphalt plant for no payment other than the cost
savings between the total amount the asphalt plant
actually paid for oil using its former burner during
the last two years and the total amount it will pay
for oil using the Hotco burner during the next two
years. On installation, the plant will make an esti-
mated payment, which will be adjusted after two
years to equal the actual cost savings.
Which of the following, if it occurred, would consti-
tute a disadvantage for Hotco of the plan described
above?
(A) Another manufacturer's introduction to the
*market of a similarly efficient burner
(B) The Clifton Asphalt plant's need for more than
*one new burner
(C) Very poor efficiency in the Clifton Asphalt
*plant's old burner
(D) A decrease in the demand for asphalt
(E) A steady increase in the price of oil beginning
*soon after the new burner is installed
Thanks..............


Hotco ----> E
PS: Post the analysis also, please.....
Today's Questions


-------------------------------------------------------------------------

1) A recent report determined that although only three percent of drivers on Maryland highways equipped their vehicles with radar detectors, thirty-three percent of all vehicles ticketed for exceeding the speed limit were equipped with them. Clearly, drivers who equip their vehicles with radar detectors are more likely to exceed the speed limit regularly than are drivers who do not.

The conclusion drawn above depends on which of the following assumptions?

(A) Drivers who equip their vehicles with radar detectors are less likely to be ticketed for exceeding the speed limit than are drivers who do not.
(B) Drivers who are ticketed for exceeding the speed limit are more likely to exceed the speed limit regularly than are drivers who are not ticketed.
(C) The number of vehicles that were ticketed for exceeding the speed limit was greater than the number of vehicles that were equipped with radar detectors.
(D) Many of the vehicles that were ticketed for exceeding the speed limit were ticketed more than once in the time period covered by the report.
(E) Drivers on Maryland highways exceeded the speed limit more often than did drivers on other state highways not covered in the report.

-------------------------------------------------------------------------

2) There is a great deal of geographical variation in the frequency of many surgical procedures-up to tenfold variation per hundred thousand between different areas in the numbers of hysterectomies, prostatectomies, and tonsillectomies.

To support a conclusion that much of the variation is due to unnecessary surgical procedures, it would be most important to establish which of the following?

(A) A local board of review at each hospital examines the records of every operation to determine whether the surgical procedure was necessary.
(B) The variation is unrelated to factors (other than the surgical procedures themselves) that influence the incidence of diseases for which surgery might be considered.
(C) There are several categories of surgical procedure (other than hysterectomies, prostatectomies, and tonsillectomies) that are often performed unnecessarily.
(D) For certain surgical procedures, it is difficult to determine after the operation whether the procedures were necessary or whether alternative treatment would have succeeded.
(E) With respect to how often they are performed unnecessarily, hysterectomies, prostatectomies, and tonsillectomies are representative of surgical procedures in general.

In 1987 sinusitis was the most common chronic medical condition in the United States, followed by arthritis and high blood pressure, in that order. The incidence rates for both arthritis and high blood pressure increase with age, but the incidence rate for sinusitis is the same for people of all ages. The average age of the United States population will increase between 1987 and 2000.

-------------------------------------------------------------------------

3) Which of the following conclusions can be most properly drawn about chronic medical conditions in the United States from the information given above?

(A) Sinusitis will be more common than either arthritis or high blood pressure in 2000.
(B) Arthritis will be the most common chronic medical condition in 2000.
(C) The average age of people suffering from sinusitis will increase between 1987 and 2000.
(D) Fewer people will suffer from sinusitis in 2000 than suffered from it in 1987.
(E) A majority of the population will suffer from at least one of the medical conditions mentioned above by the year 2000.

-------------------------------------------------------------------------

4) Parasitic wasps lay their eggs directly into the eggs of various host insects in exactly the right numbers for any suitable size of host egg. If they laid too many eggs in a host egg, the developing wasp larvae would compete with each other to the death for nutrients and space. If too few eggs were laid, portions of the host egg would decay, killing the wasp larvae.

Which of the following conclusions can properly be drawn from the information above?

(A) The size of the smallest host egg that a wasp could theoretically parasitize can be determined from the wasp's egg-laying behavior.
(B) Host insects lack any effective defenses against the form of predation practiced by parasitic wasps.
(C) Parasitic wasps learn from experience how many eggs to lay into the eggs of different host species.
(D) Failure to lay enough eggs would lead to the death of the developing wasp larvae more quickly than would laying too many eggs.
(E) Parasitic wasps use visual clues to calculate the size of a host egg.

Try this one also. it's a SC.....

An artistic presence of the first order, one frequently ranked with Picasso, Stravinsky, and James Joyce, Martha Graham was acclaimed as a great dancer long before her innovative masterworks made her the most honored of American choreographers.
(A) Martha Graham was acclaimed as
(B) Martha Graham was acclaimed to be
(C) Martha Graham's acclaim is as
(D) Martha Graham's acclaim to be
(E) Martha Graham's acclaim was in being

Try this one also. it's a SC.....

An artistic presence of the first order, one frequently ranked with Picasso, Stravinsky, and James Joyce, Martha Graham was acclaimed as a great dancer long before her innovative masterworks made her the most honored of American choreographers.
(A) Martha Graham was acclaimed as
(B) Martha Graham was acclaimed to be
(C) Martha Grahams acclaim is as
(D) Martha Grahams acclaim to be
(E) Martha Grahams acclaim was in being


I think the answer is (B)
Humanoid_nero Says
I think the answer is (B)

That's what I though. Noppe that's not the answer.....
try this. This will also be a bouncer!!


An unusually strong cyclist can, it is hoped, provide enough power to set a new distance record for human-powered aircraft in MIT's diaphanous construction of graphite fiber and plastic.
(A) can, it is hoped, provide enough power to set
(B) it is hoped, can provide enough power that will set
(C) hopefully can provide enough power, this will set
(D) is hopeful to set
(E) hopes setting


Ancient Romans found it therapeutic to bathe in cold milk, in strawberries that had been crushed, or in bathtubs filled with black caviar.
(A) to bathe in cold milk, in strawberries that had been crushed, or in bathtubs filled with black caviar
(B) that they bathe in cold milk, in strawberries that had been crushed, or in caviar that was black
(C) to bathe in cold milk, crushed strawberries, or black caviar
(D) that they bathe in cold milk, crushed strawberries, or black caviar
(E) to bathe in milk , strawberries, or caviar


Archaeologists in Ireland believe that a recently discovered chalice, which dates from the eighth century, was probably buried to keep from being stolen by invaders.
(A) to keep from
(B) to keep it from
(C) to avoid
(D) in order that it would avoid
(E) in order to keep from

Folks,

Can someone please help me with this question :

Question1 : 2 digits are taken from digits 0 to 9 (inclusive). What is the probability that the product of these 2 digits would be an even number ?

-------------------

Question 2 (variant of question 1)

A digit is drawn from digits 0 to 9 (inclusive), followed by another draw of digit. What is the probability that the product of these 2 digits is an even number when
(i) Second digit cannot be same as first digit
(ii) Second digit can be same as first digit.

Too tough for me to handle these questions. Can someone please help me with them

Folks,

Can someone please help me with this question :

Question1 : 2 digits are taken from digits 0 to 9 (inclusive). What is the probability that the product of these 2 digits would be an even number ?

Too tough for me to handle these questions. Can someone please help me with them


quick reply...will giv u the soln to next quesn also.....

q 1... even when one digit is even..or both digits are even...

so ways of choosing.. even+odd, even+even, odd+even...
if u chose even...second no. can be anything....
if u chose odd, second digit has to be even...
case 1 u chose even...5 ways...then to chose any no. ...9 ways (leaving that no....u cannot repeat i guess...) = 45 ways...

case 2...if u chose odd...5 ways....then to chose even...5 ways= 25 ways...

total ways of chosing an even pair...45+25= 70

total no. of ways to make apair...10X9=90

so probability is 70/90=7/9
is it correct???

lemme kno...
Folks,

Can someone please help me with this question :

Question1 : 2 digits are taken from digits 0 to 9 (inclusive). What is the probability that the product of these 2 digits would be an even number ?

-------------------

Question 2 (variant of question 1)

A digit is drawn from digits 0 to 9 (inclusive), followed by another draw of digit. What is the probability that the product of these 2 digits is an even number when
(i) Second digit cannot be same as first digit
(ii) Second digit can be same as first digit.

Too tough for me to handle these questions. Can someone please help me with them


Here is what I think:
As assumed by mucool, I am also assuming that the numbers cannot repeat. i.e., 11, 22, 33, 44 etc are not allowed. Also 00 is not allowed. That eliminates 10 combinations.
Total combinations possible with 10 digits = 10 x 10. Subtracting the not allowed combinations, we get total possible combinations as 90.

Since the problem says "2 digits are taken from digits 0 to 9...", I would assume that the order in which they are taken is not important. Therefore, a 4 and 5 is same as 5 and 4.

Product of 2 numbers will be even if:
1. Both numbers are even 2. One is odd and one is even.

From 0-9, we have 4 even numbers 2, 4, 6, 8 and 5 odd numbers (1, 3, 5, 7, 9)
Note that 0 is neither even nor odd.
Possible ways to get product as even:
even x even.... 4 x 3 (3 because, the number cannot repeat...like 22 or 44) = 12
odd x even... 5 x 4 = 20
Total = 20+12=32.
Probability = 32/90 = 16/45.

HTH...
Will try the next one soon..
Cheers!
Satish

As assumed by mucool, I am also assuming that the numbers cannot repeat. i.e., 11, 22, 33, 44 etc are not allowed. Also 00 is not allowed. That eliminates 10 combinations.
Total combinations possible with 10 digits = 10 x 10. Subtracting the not allowed combinations, we get total possible combinations as 90.


@satk, wont it be 82 combinations in total, instead of 90?
11,22,33,44,....99 -> 9 (Not allowed)
01,02,03,04,....09 -> 9 (Not allowed)
so total will be 100 - (9+9) = 82

Correct me if am wrong.

I think the Original sentence is Correct. THUS A .
The Correct Idiom is Acclaimed as , NOT acclaimed to be .

An artistic presence of the first order, one frequently ranked with Picasso, Stravinsky, and James Joyce, Martha Graham was acclaimed as a great dancer long before her innovative masterworks made her the most honored of American choreographers.
(A) Martha Graham was acclaimed as
(B) Martha Graham was acclaimed to be-Out-wrong Idiom
(C) Martha Grahams acclaim is as - out- 's is wrongly used
(D) Martha Grahams acclaim to be-out- worng idiom
(E) Martha Grahams acclaim was in being-out - Passive

What is the Correct answer ???

Although dozens of New Yorks small museums are either devoted to local history or various ethnic groups, there are many one-of-a-kind museums from Manhattan to the Bronx that are open for exploration on summer weekends.

(A) Although dozens of New Yorks small museums are either devoted to local history or various ethnic groups, there are
(B) Although dozens of New Yorks small museums are devoted to local history or various ethnic groups,
(C) Dozens of New Yorks small museums are devoted to local history or various ethnic groups, but there are
(D) Dozens of New Yorks small museums are devoted to local history or various ethnic groups, and there are also
(E) Devoted to local history or various ethnic groups, dozens of New Yorks small museums and also

I think answer is D.
First thing is that we have to understand the intent of the sentence. & the intent is not to CONTRAST... thus A & B are out.

C also has same flaw ( i,e Contrast by using But) - so C is also out.

E's Construction is awkward.

Hence D.

What is the Correct answer ???
@satk, wont it be 82 combinations in total, instead of 90?
11,22,33,44,....99 -> 9 (Not allowed)
01,02,03,04,....09 -> 9 (Not allowed)
so total will be 100 - (9+9) = 82

Correct me if am wrong.


@Praveen - Why do you think 01 thru 09 should not be allowed? I assumed 00,11,22,33 etc will not be allowed bcos the problem says that 2 digits are taken from 0-9...since they dont mention anything about the order, I assumed the digits are picked simultaneously. Hence, 00,11,22 etc will not b possible. They do not say anything about 01 thru 09 not being allowed.

I guess it gets confusing if you think in terms of numbers. Think of them as objects instead of numbers...that may prolly help! :)

Cheers!
Satish