Formulae and Shortcuts - making life easier!

[gazeup]

thanx guys ....

 

well i havnt taken date yet...but i will now be preprd with reccos n sop n transcripts ...so that i can apply soon after my gre is done...may be i will take gre in nov. mid

[Hermione]

Hi,

Can anyone explicitly tell me whether one needs to study topics like 'Analytical Geometry' and 'Matrices and Determinants' for GRE? I haven't seen them in any of the normal GRE prep books. However, when someone discusses it in the GRE Maths forum , I get petrified. I am a non maths student. Please help.....suja, are you reading this??

 

Hi greenhorn, sorry for my delayed reply.

 

Ya, analytical geometry is not there for GRE. I gave those formulae after one of my friends (who took her GRE last week) told me that she had to find out the minimum distance between two lines for solving one problem, and as she did not know the formula she said it took her more than 2 minutes to solve. 2 minutes is a lot of time for a non-DI problem. So, i thought i would jus put up those formulae. But sorry for giving that determinant. I shouldn't have. they are definitely not there. That was a set of formulae so i gave them all.

 

Dont let these formulae intimidate you greenhorn. They are all 'just in case' stuff. I personally believe that you dont need to know any formula to do GRE. All this is to save time for cross checking and DI problems. So dont worry if you cannot read up all these formulae (especially if you dont have much time). This thread is meant to be an archive of formulae, either directly or even remotely helpful to solve problems that might come up in GRE.

 

This is for everyone....I wanted to tell something else also here, which i think is very important. While all these formulae are meant to help you do problems quickly, never ever substitute values blindly into a formula. You can go terribly wrong if you dont plug-in data properly. And you will never know where you went wrong coz whenever we get an answer wrong, we all tend to check up our calculations rather than substitution of data. So i take this oppurtunity to just tell all you guys to use these formulae carefully. Please dont mistake me if i sound patronizing. I am telling this out of the responsibility i feel.. If any of you guys go wrong coz you used a formula that was put up in this thread, i would really feel guilty. so be careful. :)

[bscout]

I agree completely with Suja. Like the old saying: if it is good: better more, than less.

[greenhorn]

Hi,

I wish to thank 'suja' and 'man with the mission' for so unambiguously explaining matters. I really feel relieved now. Thanks a lot...

[R kapoor A]

Standard eviation Question:

The mean salary of 5 people is x , and the actual salary of two more people is x each.

Calculate the difference in SD of the 5 people and the 7 people.

[bscout]

R Kapoor you put your question in the wrong thread.

[parag_bhadra]

Multiplication of 2digit by 2 digit number

 

 

ab

x cd

------

pqrs

 

1. first multiply bd - write down the unit fig at s carry over the tens fig.

2. Multiply axd & bxc add them together and also add the carry over from step 1 write down the units fig at r and carry over the tens fig.

3. Multiply axc and add the carry over from step 2. write down at pq.

 

Its a bit difficult to explain in text - just do it a copule of times and you will get a hang of it.

 

Bye

 

Parag

[Hermione]

I found this 'Mnemonic for All Special Angles' in http://oakroadsystems.com

this might be useful to solve some geometry problems

For angle A = 0, 30° (π/6), 45° (π/4), 60° (π/3), 90° (π/2):

 

sin A = (sqrt0)/2, (sqrt1)/2, (sqrt2)/2, (sqrt3)/2, (sqrt4)/2

cos A = (sqrt4)/2, (sqrt3)/2, (sqrt2)/2, (sqrt1)/2, (sqrt0)/2

tan A = 0, (sqrt3)/3, 1, sqrt3, undefined

 

In any triangle:

sine = (opposite side) / hypotenuse

cosine = (adjacent side) / hypotenuse

tan = (opposite side)/(adjacent side) = (sine/cosine)

[spring_2006]

Thanks Sujatha for starting and building such a informative thread...and when I say this I am sure I speak on behalf of all the TMians....keep up the good work [clap] :tup:

[goodgirl]

Goodgirl,

Sorry for being late. Anyways,

If 2 trains (or bodies) start at the same time from points A and B towards each other and after crossing they take a and b sec in reaching B and A respectively, then

 

(A's speed) : (B's speed) = (root(b) : root(a))

where a and b number of seconds.

 

Hope you do get it goodgirl . All the best :)

Btw, thanks manasi for helping her on behalf of me.

thank u a lot manwiththemissio2005 and manasi.all the best 4 ur exam.

[Hermione]

1. If two events are mutually exclusive (i.e. they cannot occur at the same time), then the probability of them both occurring at the same time is 0. then: P(A and B) = 0 and P(A or B) = P(A) + P(B)

 

2. if two events are not-mutually exclusive (i.e. there is some overlap) then: P(A or B) = P(A) + P(B) - P(A and B)

 

3. If events are independent (i.e. the occurrence of one does not change the probability of the other occurring), then the probability of them both occurring is the product of the probabilities of each occurring. Then: P(A and B) = P(A) * P(B)

 

4. If A, B and C are not mutually exclusive events, then P(A or B or C) = P(A) + P(B) + P© - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)

 

and = union

or = intersection

sorry for making the formulae clusmsy using this 'and' and 'or'.

[manwiththemission2005]

The harmonic mean of x1,...,xn is

 

n / (1/x1 + ... + 1/xn)

As the name implies, it's a mean (between the smallest and largest values). An example of the use of the harmonic mean: Suppose we're driving a car from Amherst (A) to Boston (B) at a constant speed of 60 miles per hour. On the way back from B to A, we drive a constant speed of 30 miles per hour (damn Turnpike). What is the average speed for the round trip?

 

We would be inclined to use the arithmetic mean; (60+30)/2 = 45 miles per hour. However, this is incorrect, since we have driven for a longer time on the return leg. Let's assume the distance between A and B is n miles. The first leg will take us n/60 hours, and the return leg will take us n/30 hours. Thus, the total round trip will take us (n/60) + (n/30) hours to cover a distance of 2n miles. The average speed (distance per time) is thus:

 

2n / {(n/60) + (n/30)} = 2 / (1/20) = 40 miles per hour.

The reason that the harmonic mean is the correct average here is that the numerators of the original ratios to be averaged were equal (i.e. n miles at 60 miles/hour versus n miles at 30 miles/hour). In cases where the denominators of two ratios are averaged, we can use the arithmetic mean.

 

This is another good site on harmonic mean :

 

http://mathforum.org/library/drmath/view/57565.html

 

 

Cheers!!!!

 

[charanya]

Hope this link might be of use:(formulae)

http://library.thinkquest.org/20991/gather/formula/index.html

[syedjasim]

hi all, me thinx time for my contribution.( but its nothing compared to some of ur posts .still u may find them useful)

 

* Product of 2 numbers is the produst of their LCM & HCF.

 

* LCM of a fraction = LCM of numerator/HCF 0f denominator.

 

*HCF of a fraction = HCF of numer./LCM of denom.

 

 

Ratio & Proportion:

 

* if a/b = c/d = e/f = .....

 

then, a/b = c/d = e/f =(a+c+e+...)/(b+d+f+...)

 

* If a/b = c/d,

 

Then,

 

i) b/a = d/c

 

ii) a/c = b/d

 

iii) (a+b)/ b = (c+d)/d

 

iv) (a-b)/b = (c-d)/d

 

v) (a+b)/(a-b) = (c+d)/(c-d)

[Hermione]

Good job MWM, charanya and syedjasim!!!

:tup:

[parag_bhadra]

Money in Compound Interest gets doubled in 70/r years (approximately)

 

ie. P(1+r/100)^N = 2P when N=70/r

 

 

Got this in OG11 for GMAT. Checked it for full range of N & r in Excel. Seems to work fine. Would be great if someone can give a derivation for the calculation.

 

Parag

[Hermione]

1. If two events are mutually exclusive (i.e. they cannot occur at the same time), then the probability of them both occurring at the same time is 0. then: P(A and B) = 0 and P(A or B) = P(A) + P(B)

 

2. if two events are not-mutually exclusive (i.e. there is some overlap) then: P(A or B) = P(A) + P(B) - P(A and B)

 

3. If events are independent (i.e. the occurrence of one does not change the probability of the other occurring), then the probability of them both occurring is the product of the probabilities of each occurring. Then: P(A and B) = P(A) * P(B)

 

4. If A, B and C are not mutually exclusive events, then P(A or B or C) = P(A) + P(B) + P© - P(A and B) - P(B and C) - P(C and A) + P(A and B and C)

 

and = union

or = intersection

sorry guys, 'and' is intersection and 'or' is union

-suja

[Hermione]

Divisibility by:

 

2 If the last digit is even, the number is divisible by 2.

3 If the sum of the digits is divisible by 3, the number is also.

4 If the last two digits form a number divisible by 4, the number is also.

5 If the last digit is a 5 or a 0, the number is divisible by 5.

6 If the number is divisible by both 3 and 2, it is also divisible by 6.

7 Take the last digit, double it, and subtract it from the rest of the number; if the answer is divisible by 7 (including 0), then the number is also.

8 If the last three digits form a number divisible by 8, then so is the whole number.

9 If the sum of the digits is divisible by 9, the number is also.

10 If the number ends in 0, it is divisible by 10.

11 Alternately add and subtract the digits from left to right. If the result (including 0) is divisible by 11, the number is also.

Example: to see whether 365167484 is divisible by 11, start by subtracting:

3-6+5-1+6-7+4-8+4 = 0; therefore 365167484 is divisible by 11.

12 If the number is divisible by both 3 and 4, it is also divisible by 12.

13 Delete the last digit from the number, then subtract 9 times the deleted digit from the remaining number. If what is left is divisible by 13,then so is the original number.

 

TAKEN FROM DR. MATH

[priyankagre2005]

Thanks suja I was looking for these.

[manwiththemission2005]

Thanks suja. You seem to be helping us a lot even after your exams.

[Hermione]

Thanks priyanka and MWM.

@MWM - I feel like part of TM and i think i will be around for even longer time, (probably in terms of years) unless i become too busy to even come online. :)

[Hermione]

http://mathforum.org/dr.math/faq/faq.two.trains.html

i saw this in Dr. math. i thought it would be very useful for people who have a problem doing the 'two-trains' type problems...

-suja

[Hermione]

http://tinypic.com/dxmu07.jpg

PS: @non- math students--no worries!!! this is very basic stuff on conics. dont bother abt the complex diagrams, though it would be useful to know the equations of these...

 

just in case you see them in your GRE, you should be able to recognise that they are parabola or ellipse, etc. (you might have noticed that there is one problem concerning a parabola in powerprep. you need not know these equations to solve anything, but if you can recognize the equation of a conic section, it might be useful...)

 

taken from math2.com or something like that... i dont remember it exactly. i have given it after extensive editing....

 

-SUJA

[Hermione]

Hi people!

 

I was just going through the whole thread to see if there had been any mistakes or typos in any of the formulae posted here. I couldnt find any that havent already been identified by fellow TMians. But i thought i would just list them all here so that no one misses any corrections.

 

Post #7 - correction posted in #39*

post #9 - clarifications posted in #44 and #45

post #61 - correction posted in #67*

 

*looks like i am the only one who made mistakes :blush:

 

I also request other TMians to spare some time to go through the formulae once and see if any more corrections need to be made... I might have missed a few errors.

 

Thanks!

-suja.

[Hermione]

1. Mean of a distribution x1, x2, x3, ......, xn is given by the formula:

http://mathworld.wolfram.com/images/equations/Mean/equation1.gif

where n is the number of terms in the given set.

 

2. Median value of an ordered distribution y1, y2, y3, ......., yn-1, yn can be given as:

http://mathworld.wolfram.com/images/equations/StatisticalMedian/equation1.gif

 

3. Mode is the most common value obtained (or value that occurs at highest frequency) in a set of observations.

 

4. The sample variance may be computed as

http://mathworld.wolfram.com/images/equations/Variance/equation4.gif

where http://mathworld.wolfram.com/images/equations/Variance/inline12.gif is the sample mean.

 

5. The square root of the sample variance of a set of N values is the sample standard deviation

http://mathworld.wolfram.com/images/equations/StandardDeviation/equation2.gif

 

A nice link for statistics: http://mathworld.wolfram.com/topics/ProbabilityandStatistics.html