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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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.

Download GMAT Math and CR questions with Solutions from Instructors and High-scorers:
https://www.beatthegmat.com/download-gma ... 59366.html

-----------

GO GREEN..! GO VEG..!

Daily Quote:
"Stop feeling sorry for the Butcher if you had to go Veg. The butcher can find another job but the poor animal cannot get back its life"

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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

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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viju9162: Master | Next Rank: 500 Posts; Posts: 434; Joined: Mon Jun 11, 2007 9:48 pm; Location: Bangalore; Thanked: 6 times; GMAT Score:600

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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sehrish_dogar: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Jun 15, 2010 4:22 amFollowed by: 1 member; Location: Hyderabad, Pakistan; Thanked: 2 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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viidyasagar: Community Manager; Posts: 156; Joined: Mon Oct 22, 2007 6:06 amFollowed by: 3 members; Location: Mumbai, India; Thanked: 16 times; GMAT Score:700

by viidyasagar » Thu Jun 17, 2010 4:23 pm

Echo Testluv's comments.....Pradeep - u are simply AWESOME

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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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papgust: Community Manager; Posts: 1537; Joined: Mon Aug 10, 2009 6:10 pmFollowed by: 252 members; Thanked: 653 times

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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