Papgust's GMAT MATH FLASHCARDS directory

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by papgust » Tue Jun 15, 2010 6:00 pm
Thank you very much, Deepak :) !!

--

Folks, That's the end of "Averages" chapter. I will start posting in "RATIOS". There are a few important points to be noted which may be useful to you in the exam.
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by papgust » Tue Jun 15, 2010 6:07 pm
RATIOS:


1. a:b = a/b
Value of ratio remains unchanged when multiplied/divided,
a/b = a*m / b*m = (a/m) / (b/m)

2. If a/b = c/d = e/f, then each of these ratios is equal to a+c+e / b+d+f

3. If a/b = c/d, then b/a = d/c [Invertendo Rule]

4. If a/c = b/d, then a/b = c/d [Alternendo Rule]

5. If a/b = c/d, then a+b / b = c+d / d [Componendo Rule]

6. If a/b = c/d, then a-b / b = c-d / d [Dividendo Rule]

7. The compound of a:b and c:d is a*c:b*d

8. If a:b :: c:d, then a*d = b*c

9. If a:b:c :: d:e:f, then a/d = b/e = c/f = K (a constant)
Last edited by papgust on Sun Jun 20, 2010 3:35 am, edited 1 time in total.
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by viju9162 » Tue Jun 15, 2010 8:39 pm
really !! You don't know papgust how helpful this is!! I am daily making notes from your posts. It is a one stop for the flash cards ... Please keep it going....

Don't stop :)!!!!!!!

regards,
Viju
"Native of" is used for a individual while "Native to" is used for a large group

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by papgust » Tue Jun 15, 2010 8:43 pm
papgust wrote:Example:

|x+y| < |x| + |y|


1. If x and y have SAME SIGNS, then both sides will be equal.

2. If x and y have DIFFERENT SIGNS, then right side will be greater.
Folks,

There is a small typo error in the 2nd point. It should be 'right' side and not 'left' side.

I've edited the original post now. Thank you!
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by papgust » Tue Jun 15, 2010 8:48 pm
viju9162 wrote:really !! You don't know papgust how helpful this is!! I am daily making notes from your posts. It is a one stop for the flash cards ... Please keep it going....

Don't stop :)!!!!!!!

regards,
Viju
Thank you very much viju :)!
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by sehrish_dogar » Wed Jun 16, 2010 5:58 am
I'm so thankful to you for starting this post :)
God bless!

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by papgust » Thu Jun 17, 2010 6:44 am
sehrish_dogar wrote:I'm so thankful to you for starting this post :)
God bless!
Thank you sehrish :)


--


That's the end of "Ratios" chapter. I will now move to the next chapter "SEQUENCES and PROGRESSIONS".
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by viidyasagar » Thu Jun 17, 2010 4:23 pm
Echo Testluv's comments.....Pradeep - u are simply AWESOME

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by papgust » Fri Jun 18, 2010 6:21 am
Thank you vidyasagar! :)

Coming back the flashcards.


---


Arithmetic Progressions:


i. To find a term, tn = a + (n-1)*d,
where a is the first term of the series, n is the number of terms in the series and d is the constant difference between any 2 consecutive terms of the series.


ii. Average of the AP series = (First Term + Last Term)/2

--[This is applicable to the concept - Evenly Spaced Sets. Please refer this post]--


iii. Sum of the AP series, Sn = n/2 * [2a + (n-1)*d]
OR
Sn = n/2 * [a + tn]
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by papgust » Fri Jun 18, 2010 6:26 am
If a constant number (C) is added/subtracted from each term of an AP, then

i. Resulting sequence is also AP.
ii. Common difference (d) remains constant.
iii. Sum of the NEW series = Sum of the OLD series + (n * C) [where n -> No. of terms in the series]



If a constant number (C) is multiplied/divided by each term of an AP, then

i. Resulting sequence is also AP.
ii. Common difference (d) = C * Old Common difference
iii. Sum of the NEW series = C * Sum of the OLD series
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by papgust » Fri Jun 18, 2010 6:29 am
If a1, a2, ... an and b1, b2, ... bn are two AP's A and B, then

I. (a1+b1, a2+b2, ... an+bn) is ALSO an AP.
II. Common Difference (d) = Sum [d(A) + d(B)] --------- Where d(A) is the common difference of series A and d(B) is the common difference of series B
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by papgust » Sat Jun 19, 2010 8:17 pm
Geometric Progressions:


i. To find a term, tn = a * r^(n-1),
where a is the first term of the series, n is the number of terms in the series and r is the common ratio of the series.


ii. Sum of the GP series,
Sn = a * (r^n - 1) / r-1 .....[ If r > 1 ]
Sn = a * (1 - r^n) / 1-r .....[ If r < 1 ]


iii. Sum of the indefinite GP (A series that doesn't have an end)
Sn = a / (1-r)
Last edited by papgust on Sat Jun 19, 2010 8:19 pm, edited 1 time in total.
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by papgust » Sat Jun 19, 2010 8:19 pm
If a fixed non-zero constant is multiplied with each term of GP, then

i. Resulting sequence is also GP
ii. Same Common ratio.
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by papgust » Sat Jun 19, 2010 8:20 pm
If a1, a2, ... an and b1, b2, ... bn are two GP's A and B, then

I. (a1*b1, a2*b2, ... an*bn) is ALSO a GP.
II. Common Ratio (r) = r(A) * r(B) --------- Where r(A) is the common ratio of series A and r(B) is the common ratio of series B
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by papgust » Sat Jun 19, 2010 8:22 pm
That's the end of "Series & Progressions". I will start posting flashcards on the next chapter "SET THEORY".
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