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.

## Papgust's GMAT MATH FLASHCARDS directory

- papgust
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**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 ac :: 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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- viju9162
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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

Don't stop !!!!!!!

regards,

Viju

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

- papgust
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Folks,papgust wrote:Example:

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

1. If x and y haveSAME SIGNS, then both sides will beequal.

2. If x and y haveDIFFERENT SIGNS, thenrightside will begreater.

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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Thank you very much viju !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

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- papgust
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Thank you sehrishsehrish_dogar wrote:I'm so thankful to you for starting this post

God bless!

--

That's the end of "Ratios" chapter. I will now move to the next chapter "SEQUENCES and PROGRESSIONS".

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- papgust
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Thank you vidyasagar!

Coming back the flashcards.

---

i. To find a term,

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 =

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

iii. Sum of the AP series,

OR

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

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If a constant number (C) is

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

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

**added/subtracted**from each term of an AP, theni. 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, theni. 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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If

I. (

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

*a1, a2, ... an*and*b1, b2, ... bn*are two AP's A and B, thenI. (

*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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**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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If a fixed non-zero constant is

i. Resulting sequence is also GP

ii. Same Common ratio.

**multiplied**with each term of GP, theni. Resulting sequence is also GP

ii. Same Common ratio.

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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

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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That's the end of "Series & Progressions". I will start posting flashcards on the next chapter "SET THEORY".

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