Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.5)

5. 

1397 x 1397 = ?

[A]. 1951609
[B]. 1981709
[C]. 18362619
[D]. 2031719
[E]. None of these

Answer: Option A

Explanation:

1397 x 1397 = (1397)2
= (1400 - 3)2
= (1400)2 + (3)2 - (2 x 1400 x 3)
= 1960000 + 9 - 8400
= 1960009 - 8400
= 1951609.

Tamil said: (Apr 15, 2011)  
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

Jay Vaghela said: (May 30, 2011)  
Where is come form 1400 ?

G.M.L.Genatus said: (Jun 27, 2011)  
Just take a nearest whole value.

Abi said: (Aug 20, 2011)  
Hai tamil, your explanation is nice.

Malik said: (Oct 8, 2011)  
Can someone make me understand this line = (1400)2 + (3)2 - (2 x 1400 x 3) ?

Madhu said: (Oct 21, 2011)  
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

Sunil said: (Dec 12, 2011)  
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.

Sapna said: (Feb 1, 2012)  
Very good explanation sunil.

Sharon said: (Feb 7, 2012)  
Dear Tamil your explanation is good.

But please explain me from where do that 3 comes?

Kriti said: (Jul 16, 2012)  
Well, the given explanation is in the form of (a-b) ^2=a^+b^-2ab. Which is easier to solve.

Dr R Vasudevan said: (Jan 23, 2013)  
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.

G.Sravani said: (Aug 10, 2013)  
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 "

Satish Reddy said: (Sep 23, 2013)  
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).

Rahul Jadhav said: (Sep 25, 2013)  
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.

Sonal said: (Sep 13, 2014)  
@Sravani.

How can you calculate the number of 779?

Can you explain it again?

Prashant said: (Feb 15, 2015)  
Shortcut: Digital sum (D. S) method i.e 4.

D.S of 1397 is 2, so 1397*1397 is 2*2 = 4.

Now out of all the options the D.S of option a is 4.

Thukki said: (Apr 12, 2016)  
In shortcut method:

Digital sum (D. S) method i.e 4.

D.S of 1397 is 2, so 1397*1397 is 2*2 = 4.

Now out of all the options, the D.S of option a is 4.

Esai said: (Jun 8, 2016)  
Explain me about digit sum method.

Naresh said: (Jun 25, 2016)  
@Thukki.

Digital sum means?

Gore said: (Jul 13, 2016)  
@Tamil.

Your answer is perfect.

Surya said: (Jul 18, 2016)  
Hello, @Thukki.

Thank you for sharing about Digital Sum method. What if the option has another number which also have 4 as Digital Sum. Will this work foe all the problems?

Vikas Pathak said: (Nov 19, 2016)  
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.

Smile said: (Nov 27, 2016)  
@Thukki.

What is digital sum how we get num 4 above.

Rinki said: (Dec 22, 2016)  
Easy explanation. Thank you all.

Baskar said: (Dec 26, 2016)  
Can you explain logic @Prashant.

Nagarjuna Goud said: (Jan 2, 2017)  
Hi @Sravani.

I did not understand your answer how it came?

Sindu said: (Mar 10, 2017)  
1397*1397= (1397*1000)+(1397*400)-(1397*3) = 1951609.

Split 1397 as (1000+400-3).

Kabita said: (Jun 18, 2017)  
@Sindu.

Please tell me How 3 came?

Jaishanth said: (Jun 23, 2017)  
@Kabita.

We should just minus the 3 from 1400 to make the formula=(a-b)^2.
1397=(1400-3).

Pratheev Kalyan said: (Jul 9, 2017)  
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.

Rohit said: (Jul 12, 2017)  
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.

Isha said: (Jul 21, 2017)  
1+3+9+7=20 =>2+0=2.
1+3+9+7=20 =>2+0=2.
2+2=4.
a) 1+9+5+1+6+0+9=31 =>3+1=4 (4 equal to 4) so it is answer.
b)1+9+8+1+7+0+9=35 =>3+5=8 (8 not equal to 4) wrong.

Sowmi said: (Jul 23, 2017)  
Nice explanation @Rahul Jadhav.

Ajith said: (Feb 1, 2018)  
@Isha.

Whether it is applicable to all type of problems like this?

Shweta said: (May 5, 2018)  
Nice explanations thank you all.

Rohini said: (Jun 9, 2018)  
Thank you all for explaining the solution.

Aruna said: (Jun 16, 2018)  
1397*1397=?
1+3+9+7=20=2+0=2.
1+3+9+7=20=2+0=2.
2*2=4.

Option
A, 1951609 because
1+9+5+1+6+0+9=31=3+1=4 so it is the answer.

Venkat Reddy Mula said: (Jul 2, 2018)  
@Aruna.

Your method is perfect, Thanks.

Atif said: (Jul 27, 2018)  
1397 * 1397 = 1951609.

Akshay said: (Sep 4, 2018)  
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.

Sitaram said: (Dec 18, 2018)  
Very easy method, Thanks @Aruna.

Kiran said: (Jan 24, 2019)  
How come 1400?

Chethan Prabhu said: (Feb 22, 2019)  
@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.

Rishi said: (Apr 15, 2019)  
Nice explanations. Thanks all.

Pramod said: (Jun 19, 2019)  
1397=1+3+9+7=20.
1397=1+3+9+7=20.

20*20=400=4+0+0=4.

From options
A) 1951609=1+9+5+1+6+0+9=31,
3+1=4.
4 = 4. Hence ANSWER.

Deepmars said: (Jul 4, 2019)  
Good explanation, thanks @Pramod.

Sagar said: (Sep 14, 2019)  
@Aruna.

Easy, thanks for solving it.

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