hey!! everyone there are loads of calculations in the cat exam, whether is quants or di section. some of them are really very long but if done with some shortcuts, can save 25-30 seconds and shortcuts if followed in the entire exam can save 7-8 mi…
hey!! everyone there are loads of calculations in the cat exam, whether is quants or di section. some of them are really very long but if done with some shortcuts, can save 25-30 seconds and shortcuts if followed in the entire exam can save 7-8 min that means 2-3 more ques which can change the entire score.
so please post if any such shortcut is available for the calculations of squares, square roots, multipying 3 digits number, solving complex percentages..
What is the best method to find cube of a number.
well, here is a shortcut method for finding the square i saw in time material.
we all know how to find the squares of the multiples if 5.
now proceeding with that te=here 4 other types of no.(which are not the multiples of 5) whose square we need to find.
now we are left with the nos of form 5n+1,5n+2,5n-1,5n-2.
i'll deal them 1 by 1 so that there's no confusion.
nos of form 5n+1
let me tell this with an example
for eg we have 76^2
we proceed in this way (75)^2 is 5625 and in this if we add the 76th odd no. we get the square of 76. now 76th odd no. is found by using 2k+1 where k is odd no we have to find here the value of k is 76. hence 5625+151= 5776
This is valid for the 3 digit nos also for eg we have to find square of 131
square of 130 is 16900 and the 131st odd no is 261, the addition gives 17261.
nos of form 5n+2
eg we have to find the square of 47
we know the square of 45 is 2025 now we have to add the 46th as well as the 47 th odd no. for whih the result used is 4k where k is the same value that we used in the previous calculation. i.e in this the
k is 46(not 47) hence 4*46 is 184 and on adding it to 2025 we get 2209..
another eg. 182^2
180^2 is 32400 we all know
and 182nd odd no is 724(181*4)
hence 32400+724 gives 331024..
nos of form 5n-1
for eg we have to find the square of 74
we all know the square of 745 is 5625.
now square of 75 can also be obtained by adding 75th odd no to the square of 74.
therefore applying the reverse procdure and subtracting the 75th odd no from the square of 75.
5625-149=5476 which is the ans.
another eg is 129^2
130^2=16900 now subtracting the 130th(ie 259) odd no we get 16641.
nos of form 5n-2
for eg we have to find the square of 88
now recall the concept that was used in finding squares of form 5n+2.
it was got by addind 4 times 5n+1. now applying here. to find 90^2 from 88^2, we have to add 89th odd no and 90th odd no.
therefore subtracting the 89th and 90th odd no from 90^2 we can reach 88^2. we have a direct result 90^2-4k where k is the no immediately after the the number whose square is required in this case its 88
hence 8100-356=7744
eg we have 73^2
which is got by 5625(which is 75^2)-296(which is 74*4)=5329
now after you have found out the squares there is still a very slight doubt regarding the accuracy.
here's the thing that i havent read or hears anywhere or any book but ive myself observed it. it's a method to verify that whether the square u've calculated is right or not.
so here's a method.
all the nos can be written in the form 3y,3y+1,3y+2 where y is any natural no.
now all the nos of form 3y will give square which is multiple of 9(not 3). you can add up the digits n check.
the nos of form 3n+1 and 3n+2 will give a square which will be of form 3t+1 where t is again any natural no. means if u'll add up the digits till the last it will give either 1,4,7.
lets take eg. square of 129 is 16641 which is multiple of 9
sqr of 43 which is of 3y+1 form is 1849 which is of form 3t+1
sqr of 73 which is of 3y+2 form is 5329 which is of form 3t+1.
if by chance u get a no. of form 3t+2, ur ans is wrong.
if smbdy wants a proof of this i can provide that..
( need simpler way of solving this )A vessel contains a mixture of milk & water in the respective ratio 3:1 . 32 ltrs of mixture was taken out and replaced with the same quantity of milk so that the resultant ratio between the quantities of milk and water in the mixture was 4:1 respectively. If 10 ltrs of mixture is again taken out from the vessel,what is the resultant quantity of water in the mixture ? ( in ltrs)
a) 24 b) 30 c) 20 d) 36 e) 32
a man travels upsteam in a boat from one palce to another and comes back to downstream to same place in 6 hrs. total distance coverd on each side is 60 km. speed while going upsteam is one fourth of speed while goind downstream.diff b/w upstream and downstream speed?