Quantitative Reasoning

Thank you very much, Deepak !!

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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.

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)

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

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!

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 !

I'm so thankful to you for starting this post
God bless!

sehrish_dogar wrote:I'm so thankful to you for starting this post
God bless!

Thank you sehrish


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

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

Thank you vidyasagar!

Coming back the flashcards.


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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]

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

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

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)

If a fixed non-zero constant is multiplied with each term of GP, then

i. Resulting sequence is also GP
ii. Same Common ratio.

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

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