Aptitude - Numbers - Discussion

This method of converting the nmber to nearest whole and make all the calculation W.R.T (a^2-b^2).

I think, Cris Cross method is much simpler to all, as we start getting values from unit place so we dont have to find all the digits. Find one check the option, second number check the option, and so on..
1397
*1397
--------
(AL MULTIPICATION ARE DONE W.R.T LOWER NUMBER )
1) Unit place = 7*7 = 49 (put 9 in unit place and 4 as carry for next step)
(Observe the option, all have 9 in
unit place, so carry on for next
value.)

2) tens place = (7*9 + 9*7) = 63 + 63 + 4 = 130
(Put 0 in Tens place and 13 as carry for next step if required)
( the 4 in the addition comes from above step carry)
answer till now is 09
(Check the options.....only 2 are with this
digits, so step 3....)

3) hundreds place = (7*3 + 3*7 + 9*9) = 21 + 21 + 81 + 13 = 136
(13 is carry from privous step.)
(Again put 6 in 100's pace and 13 as carry
for nxt step.)
answer till this stage is 609
(check the options.... only one option
matching this number so no
more calculation)
answer is A.

eg : if digits are abcd * wxyz
1) here (d*z) gives unit place number.
2) (z*c + y*d)gives tens place number.
3) (z*b + x*d + y*c) gives hundred place number.
4) (z*a + w*d + y*d + x*c)gives thousand number.
(OBSERVE THE TRICK)
5) (y*a + w*c + x*b) given nxt number to left.
6) (x*a + w*b) give nxt number.
7) (w*a) gives last number.
(Please note when ever you get CARRY from one STEP please add That Carry to The Step Followed after that step)
e.g: if step 1 results 57 as the answer put 7 at unit place and carry 5 to 2 step, add this five to 2 step result and so on...
if the explanation look wierd or trouble some please google vedic maths, and the name of this method is criss cross method.

@All.

Guys don't solve this in this way. Just add the digits
Question is 1397 X 1397.
add digits
1 + 3 + 9+ 7 = 20, add again 2 + 0 = 2
So it becomes 2 X 2 = 4.

Now check options and see which sum upto 4
A) 1951609 = 1 + 9 + 5 + 1 + 6 + 0 + 9 = 31, 3 + 1 = 4. So this is the answer.
B) 1981709 = 1 + 9 + 8 + 1 + 7 + 0 + 9 = 35, 3 + 5 = 8, wrong.
C) 18362619 = 1 + 8 + 3 + 6 + 2 + 6 + 1 + 9 = 36, 3 + 6 = 9,
D) 2031719 = 2 + 0 + 3 + 1 +7 + 1 + 9 = 23, 2 + 3 = 5.

An easier method:

1397 is slightly less than 1400
1397*1397 must be slightly less than 1400*1400 = 1960000

There are only 2 numbers less than 1960000
i.e [A] 1951609 ; [C]. 18362619

[C] is too small. Hence the correct answer is (A).

Another check : tens digit : 7*7= 49 : unit digit 9, carry to tens digit 4; 7*9 = 7*9 +4 = 130 : 0 in Tens digit and 13 carried to Hundreds: (A) has 0 in Tens digit.

We have options,

So try to find the nearest answer available in the options.

If we round off 1397 we get 1400,

Just do the square of 14 and, it comes to 196.

Check the nearest answer available to figure 196 (Check the first three digit).

The 1st 3 digit of the nearest answer should be less from 196 as we have to deduct 3 from 1397.

The multiplication of sum of digits = the some of digits of the answer.
example = 24*6 = 144 =1+4+4 = 9.
now 2+4 *6 = 36= 3+6=9.

So if the answer is given we can use this method.
Now, back to question.
1397*1397
1+3+9+7 * 1+3+9+7,
=2 * 2 = 4.
And, in option, 1951609 = 1+9+5+1+6+0+9 = 4.

1397*1397=?

Since 1400*1400=1960000, so the result must be less than 1960000. By this, options c and d gets eliminated. Remaining is a and b.

The number 1397 is divisible by 11. So, the answer must also be divisible by 11. Thus option b(not divisible by 11) is eliminated and option a is the answer.

Step-1: Do the sum of the digits of multiplicands then multiply both.
Step-2: If the number comes in two-digit add them.
Step-3: Add all the digits of answer untill it becomes a single digit number.
15^2 = 225
1+5 * 1+5 = 2+2+5
6 * 6 = 9
36 = 9
3+6 = 9
9 = 9

So, the answer is 225.

If you want to multip[ly the theis type of big no follow the step:
1397 * 1397=?
1397*1400=1955800
and (1397+3=1400) so 1397*3=4191
1955800-4191=1951609

another example:
234*52
you can take 234*50=11700
and (52-2=50) so 234*2=468
11700+468=12168

1397 is slightly less than 1400.

1397*1397 must be slightly less than 1400*1400 = 1960000.

There are only 2 numbers less than 1960000.

i.e [A] 1951609 ; [C]. 18362619.

[C] is too small. Hence the correct answer is (A).

Just multiply.

1397
1397

After multiplying for the second time just add and see the last 3digits are coming to 609 then its easy to ascertain or you can take the nearest whole number, whichever seems easy for you.