**Quantitative**

**Aptitude Shortcuts and Tricks**

__Finding number of Factors__To find the number of factors of a given number, express the number as a product of powers of prime numbers.

In this case, 48 can be written as 16 * 3 = (24 * 3)

Now, increment the power of each of the prime numbers by 1 and multiply the result.

In this case it will be (4 + 1)*(1 + 1) = 5 * 2 = 10 (the power of 2 is 4 and the power of 3 is 1)

Therefore, there will 10 factors including 1 and 48. Excluding, these two numbers, you will have 10 – 2 = 8 factors.

__Sum of n natural numbers__-> The sum of first n natural numbers = n (n+1)/2

-> The sum of squares of first n natural numbers is n (n+1)(2n+1)/6

-> The sum of first n even numbers= n (n+1)

-> The sum of first n odd numbers= n^2

__Finding Squares of numbers__To find the squares of numbers near numbers of which squares are known

To find 41^2 , Add 40+41 to 1600 =1681

To find 59^2 , Subtract 60^2-(60+59) =3481

**Finding number of Positive Roots**If an equation (i:e f(x)=0 ) contains all positive co-efficient of any powers of x , it has no positive roots then.

**Eg:**x^4+3x^2+2x+6=0 has no positive roots .

__Finding number of Imaginary Roots__For an equation f(x)=0 , the maximum number of positive roots it can have is the number of sign changes in f(x) ; and the maximum number of negative roots it can have is the number of sign changes in f(-x) .

Hence the remaining are the minimum number of imaginary roots of the equation(Since we also know that the index of the maximum power of x is the number of roots of an equation.)

**Reciprocal Roots**The equation whose roots are the reciprocal of the roots of the equation ax^2+bx+c is cx^2+bx+a

__Roots__Roots of x^2+x+1=0 are 1,w,w^2 where 1+w+w^2=0 and w^3=1

**For a cubic equation ax^3+bx^2+cx+d=o sum of the roots = - b/a sum of the product of the roots taken two at a time = c/a product of the roots = -d/a**

__Finding Sum of the roots__For a biquadratic equation ax^4+bx^3+cx^2+dx+e = 0 sum of the roots = - b/a sum of the product of the roots taken three at a time = c/a sum of the product of the roots taken two at a time = -d/a product of the roots = e/a

__Maximum/Minimum__-> If for two numbers x+y=k(=constant), then their PRODUCT is MAXIMUM if x=y(=k/2). The maximum product is then (k^2)/4

-> If for two numbers x*y=k(=constant), then their SUM is MINIMUM if x=y(=root(k)). The minimum sum is then 2*root(k) .

__Inequalties__-> x + y >= x+y ( stands for absolute value or modulus ) (Useful in solving some inequations)

-> a+b=a+b if a*b>=0 else a+b >= a+b

-> 2<= (1+1/n)^n <=3 -> (1+x)^n ~ (1+nx) if x<<<1> When you multiply each side of the inequality by -1, you have to reverse the direction of the inequality.

__Product Vs HCF-LCM__Product of any two numbers = Product of their HCF and LCM . Hence product of two numbers = LCM of the numbers if they are prime to each other

__AM GM HM__For any 2 numbers a>b a>AM>GM>HM>b (where AM, GM ,HM stand for arithmetic, geometric , harmonic menasa respectively) (GM)^2 = AM * HM

__Sum of Exterior Angles__For any regular polygon , the sum of the exterior angles is equal to 360 degrees hence measure of any external angle is equal to 360/n. ( where n is the number of sides)

For any regular polygon , the sum of interior angles =(n-2)180 degrees

So measure of one angle in

Square-----=90

Pentagon--=108

Hexagon---=120

Heptagon--=128.5

Octagon---=135

Nonagon--=140

Decagon--=144

__Problems on clocks__Problems on clocks can be tackled as assuming two runners going round a circle , one 12 times as fast as the other . That is , the minute hand describes 6 degrees /minute the hour hand describes 1/2 degrees /minute . Thus the minute hand describes 5(1/2) degrees more than the hour hand per minute .

The hour and the minute hand meet each other after every 65(5/11) minutes after being together at midnight. (This can be derived from the above) .

__Co-ordinates__Given the coordinates (a,b) (c,d) (e,f) (g,h) of a parallelogram , the coordinates of the meeting point of the diagonals can be found out by solving for [(a+e)/2,(b+f)/2] =[ (c+g)/2 , (d+h)/2]

__Ratio__If a1/b1 = a2/b2 = a3/b3 = .............. , then each ratio is equal to (k1*a1+ k2*a2+k3*a3+..............) / (k1*b1+ k2*b2+k3*b3+..............) , which is also equal to (a1+a2+a3+............./b1+b2+b3+..........)

**Finding multiples**x^n -a^n = (x-a)(x^(n-1) + x^(n-2) + .......+ a^(n-1) ) ......Very useful for finding multiples .For example (17-14=3 will be a multiple of 17^3 - 14^3)

__Exponents__e^x = 1 + (x)/1! + (x^2)/2! + (x^3)/3! + ........to infinity 2 <>GP

-> In a GP the product of any two terms equidistant from a term is always constant .

-> The sum of an infinite GP = a/(1-r) , where a and r are resp. the first term and common ratio of the GP .

__Mixtures__If Q be the volume of a vessel q qty of a mixture of water and wine be removed each time from a mixture n be the number of times this operation be done and A be the final qty of wine in the mixture then ,

A/Q = (1-q/Q)^n

__Some Pythagorean triplets:__3,4,5----------(3^2=4+5)

5,12,13--------(5^2=12+13)

7,24,25--------(7^2=24+25)

8,15,17--------(8^2 / 2 = 15+17 )

9,40,41--------(9^2=40+41)

11,60,61-------(11^2=60+61)

12,35,37-------(12^2 / 2 = 35+37)

16,63,65-------(16^2 /2 = 63+65)

20,21,29-------(EXCEPTION)

__Appolonius theorem__Appolonius theorem could be applied to the 4 triangles formed in a parallelogram.

__Function__Any function of the type y=f(x)=(ax-b)/(bx-a) is always of the form x=f(y) .

__Finding Squares__To find the squares of numbers from 50 to 59

For 5X^2 , use the formulae

(5X)^2 = 5^2 +X / X^2

Eg ; (55^2) = 25+5 /25

=3025

(56)^2 = 25+6/36

=3136

(59)^2 = 25+9/81

=3481

__Successive Discounts__Formula for successive discounts

a+b+(ab/100)

This is used for succesive discounts types of sums.like 1999 population increses by 10% and then in 2000 by 5% so the population in 2000 now is 10+5+(50/100)=+15.5% more that was in 1999 and if there is a decrease then it will be preceeded by a -ve sign and likewise.

__Rules of Logarithms:__-> loga(M)=y if and only if M=ay

-> loga(MN)=loga(M)+loga(N)

-> loga(M/N)=loga(M)-loga(N)

-> loga(Mp)=p*loga(M)

-> loga(1)=0-> loga(ap)=p

-> log(1+x) = x - (x^2)/2 + (x^3)/3 - (x^4)/4 .........to infinity [ Note the alternating sign . .Also note that the ogarithm is with respect to base e ]

**Also Read:**

Thanks for the tips, very useful for students. Thank you buddy for this information. Keep it up..

ReplyDeleteIt is informative and useful information. I really appreciate your efforts. Thank you for this information. Keep it up..

ReplyDeleteGood shortcuts.. if u give some examples for each trick it will worth more

ReplyDeletegood work... keep it up!! <3

ReplyDeleteThank you for the valuble information improve your Aptitude knowledge thank you

ReplyDeleteAptitude knowledge plays a major role every where please dont loose

ReplyDeleteReally excellent!!!! Keep it up.

ReplyDeleteI am in my final year of my engineering and so 'coz of less time was looking for a quick quantitative aptitude preparation course for CAT 2012 exam. I heard much of Prof. Ravi Handa and so after searching for him found his online preparation course at http://www.wiziq.com/course/5553-speed-calculations-shortcuts-tricks-for-cat-competitive-exams

ReplyDeleteBut before enrolling for this course I want friends your expert guidance. So please review this online course for me.

Thanks !

This comment has been removed by the author.

ReplyDelete4 : 3. After 4 years this ratio will be 9 : 7. If at the time of their

ReplyDeletemarriage the ratio was 5 : 3, how many years ago they were

married?

(a) 10 years (b) 8 years

(c) 12 years (d) 15 years

16. Simplify:

1 3 1 3 1 3 1

1 3 1 3 1 3 1

. . .

. . .

. . .

. . .

× × −

× + +

(a) .3 (b) 3

1

3

(c) .

.

3 (d) 1

17. What sum of money is to be divided among 3 men in

the ratio 3 : 4 : 5 so that the third man receives Rs 10 only.

(a) Rs 56 (b) Rs 84 (c) Rs 120 (d) Rs 24

18. Sum of two numbers prime to each other is 20 and

their L.C.M. is 99. What are the numbers?

(a) 8 and 12 (b) 14 and 6

(c) 19 and 1 (d) 11 and 9

19. Find square root of 2 7.

.

(a) .5 (b) 5 (c) 1

2

3

(d) .3

20. Find the greatest of the four least common multiples

of 3, 5 and 7.

(a) 1 (b) 420 (c) 315 (d) 105

http://vkmtvpm.blogspot.in

ReplyDeleteHi. Thx.. Good Stuff!

ReplyDeleteGet more aptitude questions with explanation here...

infibee.com/general-aptitude

I was just surfing on internet and found your blog after reading this i realize that i should come here often

ReplyDeletephen 375 | phen

This comment has been removed by the author.

ReplyDeleteThis comment has been removed by the author.

ReplyDeletefor the shortcuts like mentioned here

ReplyDeletei enrolled for the perfect quantitative aptitude courseioned here only...

helps me speed calculations and many other useful tricks for CAT, XAT, SNAP, IIFT and many more :)

http://www.wiziq.com/course/5553-speed-calculations-shortcuts-tricks-for-cat-competitive-exams

Nice Info... Thx....

ReplyDeleteHi friends!

ReplyDeleteCheck this site. aptitude questions and answers with explanation.

http://www.infibee.com/general-aptitude/

good efforts dude...

ReplyDeleteHey there! Someone in my Facebook group shared this site with us so I came to give it a look.

ReplyDeleteI'm definitely enjoying the information. I'm book-marking and will

be tweeting this to my followers! Outstanding blog and brilliant design.

Review my site :: bmi chart female

I do not even know the way I finished up right here, however I believed this submit was great.

ReplyDeleteI do not realize who you are however definitely you are going to a famous

blogger should you aren't already. Cheers!

Here is my blog post: bmi chart for men

First off I would like to say wonderful blog! I had a quick question in which I'd like to ask if you do not mind. I was curious to know how you center yourself and clear your mind prior to writing. I've had a tough

ReplyDeletetime clearing my thoughts in getting my ideas out. I truly do take pleasure in writing but it just seems like the first 10 to 15 minutes are

usually wasted just trying to figure out how to begin. Any suggestions or

hints? Thanks!

Check out my blog - book of ra kostenlos spielen ohne anmeldung

My spouse and I absolutely love your blog and find most of your post's to be precisely what I'm looking for.

ReplyDeleteDo you offer guest writers to write content in your case?

I wouldn't mind writing a post or elaborating on some of the subjects you write in relation to here. Again, awesome weblog!

my site :: http://getsmarq.Com/

Link exchange is nothing else except it is just placing the other person's web site link on your page at suitable place and other person will also do same for you.

ReplyDeleteHere is my web page novoline automaten tricks 2012

It's the best time to make some plans for the future and it's time to be happy.

ReplyDeleteI have read this post and if I could I wish to suggest you some interesting things or

suggestions. Maybe you could write next articles referring to this article.

I desire to read even more things about it!

Feel free to visit my webpage ... novoline automaten tricks

It's remarkable in support of me to have a web page, which is helpful in support of my know-how. thanks admin

ReplyDeleteFeel free to surf to my web site - book ra

Everyone loves it when individuals get together and share views.

ReplyDeleteGreat site, continue the good work!

my homepage; novoline spielautomaten

Hello to every body, it's my first go to see of this web site; this webpage carries awesome and genuinely good data in favor of readers.

ReplyDeleteHere is my web page: book of ra apk boerse

I'm gone to tell my little brother, that he should also visit this webpage on regular basis to obtain updated from latest gossip.

ReplyDeleteFeel free to surf to my web-site - book auf ra

Great article! We are linking to this great article on our website.

ReplyDeleteKeep up the good writing.

Feel free to surf to my web blog ... bock of ra kostenlos spielen

Great post.It's very useful for the aptitude preparation. Thanks for sharing

ReplyDeleteAwesome post about aptitude shortcuts. It's very useful for preparation. Thanks for sharing.

ReplyDeleteExcellent aptitude Shortcut tips and trick. Thanks for sharing.

ReplyDeleteThanks for sharing the useful aptitude shortcuts.

ReplyDeleteThanks for sharing the aptitude shortcuts methods. It's very useful.

ReplyDeleteI want this type of publish which i got from your website.Thanks for posting this publish.

ReplyDeletePreparing for CAT- MBA 2014? Cracking CAT Exam is not a difficulty when one gets the guidance of highly qualified and experienced scholars. if you are wondering how to prepare for CAT Exam 2014, prepare Online in the best way for Cat Exam 2014 . Get the guidance of CAT gurus, and crack the mba entrance exam . To learn more, check : www.wiziq.com/course/9277-lr-vr-di-ds-speed-calculations-quant-general-awareness

ReplyDeleteTake a look on Quantitative aptitude questions Through http://skillgun.com

ReplyDelete