Aptitude - Square Root and Cube Root - Discussion

How Separate Into 2 x 2 x 3 x 3 x 7 x 11 The 2772?

Guys, try to solve such questions by options:


The least perfect square, which is divisible by each of 21, 36 and 66 implies that of all the options correct number should be divisible by 7, 11,2,3.
21=3x7
36=2^2X3^3
66=2x3x11


Of these four options only "1" is divisble by 7.

SO CORRECT ANSWER IS 1.

PS: If there were more than 2 choices divisble by 7, then eliminate one of them by divind them by 11 as well, and so on by the factors of the divisors. It would be your bad luck if you get multiple answers even after eliminating the options..

We should multiple it by 7 and 11 to make it a square... If you can see in the factors that 2*2 * 3*3 *7 * 11 = 2772 can not make a square until we multiply it by 7 to make 7*7 and by 11 to make 11*11.... Now 2*@ *3*3 * 7*7 *11*11 .... all are sqare ..which means (2*3*7*11)2(sqare) - (462)2(sqare) = 213444 (Ans)

@Sneha

I didn't get last 2 steps in your solution, please can you help me.

If we divide it by 2 and 3
The figuers will be 2*3*7*11

And to find it's square root is difficult

If there are words like Highest,Biggest then H.C.F. is to be taken
and if there are words like Smallest,least then L.C.F. is to be taken(though this is not an exact interpretation but it has worked in all cases)

Shall we divide it by 2 and 3 either multiplying it by 7 and 11, explain this plz anybody.

First least num that is divisible by 21,36,66 by taking l.c.m ,

We get 2772,
by taking factors 2772=2*2*3*3*7*11
as we have find least perfect square
we need to multiply with 7*11,so we can get perfect sq. near to 2772

So the soltn is 2*2*3*3*7*7*11*11 = 213444.

2 / 21 36 66
--------------------
2 / 7 18 66
---------------------
3 / 7 9 33
---------------------
3 / 7 3 11
----------------------
/ 7 1 11


2*2*3*3*7*11= 2772


pls see this way solve the problem

How 7 square and 11 square came in last step please explain?

How can we know that in which question we have to take lcm or hcf.