Aptitude - Numbers - Discussion

@Sravani.

How can you calculate the number of 779?

Can you explain it again?

If you want to multiply this type of big no follow the step:

1397 * 1397 = ?

1397*1400 = 1955800.

and (1397+3 = 1400) So 1397*3 = 4191.

1955800-4191 = 1951609.

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).

1397*1397 = 7*7=49

7*9=63
7*3 = 21
.......779
9*7 =63
9*9 = 81
3*7 = 21
.....779
.... 73
.....1
== 609

In option A contain last three digits as 609.
So Answer is " A "

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.

Well, the given explanation is in the form of (a-b) ^2=a^+b^-2ab. Which is easier to solve.

Dear Tamil your explanation is good.

But please explain me from where do that 3 comes?

Very good explanation sunil.

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.

Just that is a formula:

(a-b)^2 = a^2 + b^2 + 2ab in the same way

(1400-3)^2 = 1400^2 + 3^2 + 2*1400*3