Aptitude - Numbers - Discussion

Discussion :: Numbers - General Questions (Q.No.4)

4. 

What least number must be added to 1056, so that the sum is completely divisible by 23 ?

[A]. 2
[B]. 3
[C]. 18
[D]. 21
[E]. None of these

Answer: Option A

Explanation:

 23) 1056 (45
      92
      ---
      136
      115
      ---
       21
      ---
     
 Required number = (23 - 21)    
                 = 2.   

Loverboy said: (Dec 20, 2010)  
Explain?

Jarun James said: (Dec 28, 2010)  
Explain more.

Abhisek said: (Jan 26, 2011)  
Will you please elaborate?.

Karthi said: (Feb 21, 2011)  
The value 92, 45 how it comes.

Explain.

Deepika said: (Mar 9, 2011)  
To find the correct no to add in amt 1056 it is divided by 23 to like 23*4 = 92 & its minus from 1056 then it remains 136 then its divided by 23*5 = 115 & minus from 136 then the remaining amt is 21 so there must be add 2 no.(21+2=23) so the ramaining amt will be zero.

Jomon said: (Jun 17, 2011)  
1056/23=45.91
23*45=1035
1056-1035=21

Therefore 23-21=2
Ans =2

Nikitha said: (Aug 19, 2011)  
It is so easy..

If the number 1056 is completely divisible by 23 means, remainder should come zero..

But if we divide 1056 by 23, the remainder is 2..

So if 2 is added to the 1056, we get remainder 0.

Therefore solution is 2

Vijay Yadav said: (Sep 8, 2011)  
@Nikitha nice and thanks.

Archana said: (Sep 29, 2011)  
Very nice answer deepika. I am understood.

Hamsitha said: (Nov 12, 2011)  
Very good answer nikitha.

Suba said: (Dec 25, 2011)  
23x45=1035 so 1056-1035=21 so the number 23-21=2 this is the answer

Jaldhi said: (Feb 9, 2012)  
Why are we first dividing aren't we suppose to add the least number?

Hanipoo23 said: (Feb 23, 2012)  
Thank you nikitha.

Yogendra said: (Mar 14, 2012)  
Thanks nikitha.

Sankar said: (May 15, 2012)  
Find digital root for 1056. 1+5+6=12, 1+2= 3 digital root should be less than or equal to one. Digital root for 23 is 2+3=5 so it will of form 3/5 for to exactly divisible we need to add 2 to numerator so answer is 2.

Madhuri said: (Aug 18, 2012)  
Thank you so much sankar.

Bluemoon said: (Apr 8, 2013)  
I don't understand why we should do 23-21 at the end can anyone explain this. And @Nikitha 2 is not the remainder. 21 is the remainder.

Himanshu Jain said: (Oct 21, 2013)  
Will you please explain it a little bit better?

Roshinphilips said: (Nov 16, 2013)  
1056/23 = 45.xx,

45*23 = 1035,

1035+23 = 1058.

Difference between 1056 and 1058 = 2.

Raj said: (Feb 11, 2014)  
1056/23 = 45.91.

0.91*23 = 20.93 = 21(approx).

23-21 = 2.

Navin Kumar Kamti said: (Mar 4, 2014)  
1056/23 = 45.91.
45*23 = 1035.
Now we can write 1035+23 = 1058.

Hence,
1058-1056 = 2.

Rupesh said: (Aug 18, 2014)  
Consider first 3 digits 105.
23*4=92; 105-92=13.

Now 13 & remaining digit 6 forms 136.
23*5=115; 136-115=21.

If we are adding 2 in 21 then it will completely divisible.

Ankita said: (Dec 10, 2014)  
Consider the number 13. When we divide it by 6, the remainder is 1. Now, what must be added to 13 to make it completely divisible by 6?

12 is completely divisible by 6. We must add 6 more to 12 to make it divisible by 6. While dividing by 13, the remainder is 1. So we add 5 (6-1) more to make the number 13 divisible by 6.

Similarly in this case, we add 2 (23-21).

Rocky said: (Dec 24, 2014)  
23*46 = 1058.

Therefore if we add 2 to 1056 then it is divisible by 23.

Prashant said: (Feb 15, 2015)  
Digital sum method works here:

1056+2 = 1058--- 5 (digital sum).

1056+18 = 1074---3.

1056+3 = 1059-- 6.

1077+21 = 1098--9.

And the digital sum of 23 is 5. So option (A) is correct.

Hmt said: (Mar 28, 2015)  
If we do 1056/23. Then remainder = 21.

= 23-21 = 2.

Because to make 23 we have to add 2 in remainder. So we can do 23/23 which is 0.

Abhijit Mukherjee said: (May 8, 2015)  
@Nikitha please explain it.

But if we divide 1056 by 23, the remainder is 2.

So if 2 is added to the 1056, we get remainder 0.

Therefore solution is 2.

Ragu said: (May 31, 2015)  
Hi dude.

We have 4 choices in question paper.

Firs to add 1056+2 = 1058, 1058/23 = 0, we got no remaining in finally.

1056+3 = 1059, 1059/23 = 1 we gotta remaining.

1056+18 = 1074, 1074/23 = 16, same like got remaining.

Finally 1056+21 = 1077, 1077/23 = 19, same like got remaining.

Ans = 2.

Dinesh said: (Jul 1, 2015)  
Very good platform provided you mam to understand the problem. Really very nice!

Bhupendra said: (Oct 19, 2015)  
23^2 = 529.

And 529x2 = 1058.

Given 1056, difference = 2.

Lavanya Sankari said: (Dec 16, 2015)  
I can understand it very clearly.

Gayatri said: (Jun 1, 2016)  
Nikitha has explained well that everyone can understand easily.

Thank you @Nikitha.

Amit said: (Jun 27, 2016)  
Nice trick @Sankar.

@Ammu said: (Jul 4, 2016)  
Thank you friends. Now it's easy to understand.

Mitali said: (Jul 7, 2016)  
This digital root method is nice and quick. Does it work for all questions, where else can this be applied?

Payal said: (Jul 8, 2016)  
What must be added to 5678 to gives a remainder 35when divided by 460?

Please help me to get the solution.

Shailesh Kumar said: (Jul 15, 2016)  
I understood well with the help of these explanations.

Raghavi said: (Jul 30, 2016)  
@Sankar & @Prashant.

Is the digital root method is applicable for all the divisors?

Prasanth said: (Aug 4, 2016)  
23 * 46 = 1058.

1058 - 1056 = 2.

Sravanthi said: (Aug 16, 2016)  
Very nice explanation @Nikitha.

Kalyan said: (Aug 18, 2016)  
Nice explanation @Jomon.

Kshama Jain said: (Oct 22, 2016)  
Firstly what @Nikitha has explained is wrong. Because the remainder is 21 not 2. So please can somebody give me the answer why we did 23 - 21?

Anzer Hussain said: (Nov 3, 2016)  
1056/23 = 45.91.
So round of the figure of the result that means 46.
Then 46 * 23 = 1058.

=> 1058 - 1056 = 2.

The answer is 2.

Anil said: (Nov 25, 2016)  
What must be added to 23/5 to get 4 1/2?

Blessy said: (Feb 22, 2017)  
Explained well, Thanks @Navin Kumar.

Nirmal said: (Apr 15, 2017)  
I don't understand please anyone help me.

Nazar said: (Jun 14, 2017)  
Thank you @Nikitha.

Good explanation.

Tony said: (Jun 17, 2017)  
1+0+5+6 = 12 = 1+2 = 3.
So given divisor is 23=2+3=5.
So to make a dividend to multiple of 5, add 2 to 3, it gives 5.

Nancy said: (Jul 9, 2017)  
How you got this 23-21=2?

Adithya said: (Oct 9, 2017)  
Hi Guys, it is simple first calculate 23*46 = 1058, Then see our number it is 1056, So to get remainder as Zero we need to add 2.

Astik said: (Nov 30, 2017)  
1056/23.

=23/1056/46
92
-----------
136
138
-------------


When we multiply 23*5=115.
2
But I take one 1 more bigger digit I multiply 23*6=138
Difference of this two numbers is 2.
This is the simplest way.

Nkumar said: (Dec 4, 2017)  
1056+2=1058, it is completely divided by 23, so difference no. 1056-1058 =2, because 1058/23 =46.

Nandi Vishal said: (Feb 3, 2018)  
The best way lets assume 1056 to be 1+0+5+6=12=1+2=3 --> 1.
23=2+3=5 --> 2.

Hence 2 must be added to (1) to get completely divisible by 23.

Sunny said: (Feb 4, 2018)  
@Nikitha.

But the reminder is not 2 how it comes 2?

Ankur said: (Feb 10, 2018)  
@Nandi.

Please apply same formula in 1045 instead of 1056, 23 will remain same.

Sathish said: (Feb 18, 2018)  
Why we did 23-21?

Mohanagiri said: (May 25, 2018)  
Simple,

They are asking only which is a least number make 1056 becomes divisible by 23.
So, we know divisibility means the remainder will be zero.

First, divide the1056 by 23.

And; we know 23*6=138, hence the given number 105(6) is must be 105(8) then we divided). Hence add 2 finally we get remainder zero.

Satish Chandra said: (Jun 9, 2018)  
When 1056 divided by 23 it yields 21 but we need to get "0" as remainder if we add +2 to 21 (i.e. 1058 it gives 23 as the remainder when it gets divided by 23) and it 23 get divided by 23 yields zero "0".

Shubhada Lokhande said: (Sep 2, 2018)  
Basically we have to %(mod) operation here;

1056%23=
1056/23=45.91=46.
46*23=1058.
1058-1056=2 => answer.

Soura said: (Sep 17, 2018)  
@Mohanagiri.

Smart approach, Thanks.

Muthu said: (Jan 3, 2019)  
@ALL.

As per my method.

10 * 23 = 2300
2300/2 = 1150
1150-1056 = 94
94/23 = 4 quotient balance 2 ans is 2.

Js Parihar said: (Feb 26, 2019)  
1056/23.

The simple method is;
The digit sum of 1056 = 12 = 3,
The digit sum of 23 = 5.

So what must be added to 3 to be divisible by 5 i.e 2 is the correct answer.

Meet said: (May 1, 2019)  
How can 1056-92 be 136?

It comes 964.

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