List of EQUATIONS?

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gmatjedi: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Sat Aug 15, 2009 4:36 am; Thanked: 19 times

by gmatjedi » Sun May 16, 2010 3:07 pm

Has any member compiled and posted a list of EQUATIONS/PROCESSES that would be helpful in the Quant Section?
Below are listed a few interesting equations/processes that I came across.

1. Area of the triangle when coordinates of the vertices are (x1, y1), (x2, y2), (x3, y3)
= {|x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2)|}/ 2
(from Rahul)

2. Generally, the smallest prime factor of h(n)+1 is larger than n/2.
(from cneal4 )

I hope each of us can share important formulas and/or processes that would enable solving the more difficult quant questions.

It could serve as a great resource for the community.

Source: Beat The GMAT — Problem Solving | Sun May 16, 2010 3:07 pm

sanju09: GMAT Instructor; Posts: 3650; Joined: Wed Jan 21, 2009 4:27 amFollowed by: 80 members; Location: India; Thanked: 267 times; GMAT Score:760

by sanju09 » Mon May 17, 2010 12:31 am

gmatjedi wrote:Has any member compiled and posted a list of EQUATIONS/PROCESSES that would be helpful in the Quant Section?
Below are listed a few interesting equations/processes that I came across.

1. Area of the triangle when coordinates of the vertices are (x1, y1), (x2, y2), (x3, y3)
= {|x1 (y2 - y3) + x2 (y3 - y1) + x3 (y1 - y2)|}/ 2
(from Rahul)

2. Generally, the smallest prime factor of h(n)+1 is larger than n/2.
(from cneal4 )

I hope each of us can share important formulas and/or processes that would enable solving the more difficult quant questions.

It could serve as a great resource for the community.

Do you know that primes 41 and past are found by putting n = 1, 2, 3, 4, 5, ... in the prime function P (n) = n^2 - n + 41? But, it fails after some positive integer value of n. What is that n?

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gmatjedi: Senior | Next Rank: 100 Posts; Posts: 85; Joined: Sat Aug 15, 2009 4:36 am; Thanked: 19 times

by gmatjedi » Mon May 17, 2010 3:54 pm

thanks sanju.
not sure what the answer is.
how do you calculate it?

Another formula:
The Set Theory Formula to get the exact unique count in one set is :

P(A) + P(B) + P(C) - 2P(AnB) - 2P(AnC) - 2P(BnC) + 3P(AnBnC)
(from rn4 gmat)

sumanr84: Legendary Member; Posts: 758; Joined: Sat Aug 29, 2009 9:32 pmFollowed by: 2 members; Location: Bangalore,India; Thanked: 67 times

by sumanr84 » Mon May 17, 2010 8:27 pm

gmatjedi wrote:thanks sanju.
not sure what the answer is.
how do you calculate it?

Another formula:
The Set Theory Formula to get the exact unique count in one set is :

P(A) + P(B) + P(C) - 2P(AnB) - 2P(AnC) - 2P(BnC) + 3P(AnBnC)
(from rn4 gmat)

I think the above formula is not correct,
If you have 3 set such as A,B and C and you are told to find the total then you can apply the below formula,

Total = P(A) + P(B) + P(C) - 2P(AnB) - 2P(AnC) - 2P(BnC) + P(AnBnC) [ add the singles, subtract the doubles, and add back one triple]

Now to get unique count in one set you need to subtract from Total.

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