What is the remainder when the square of N divided by 5 N divided by 5 leaves a remainder 3?

Discussion :: Numbers - General Questions (Q.No.31)

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31.

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?

Answer: Option D

Explanation:

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.

x = 5k + 3

x2 = (5k + 3)2

= (25k2 + 30k + 9)

= 5(5k2 + 6k + 1) + 4

On dividing x2 by 5, we get 4 as remainder.

Rajesh Rao.v said: (Sep 2, 2010)
X = 5+3 = 8 square of 8 = 64 then 64/5 remainder is 4.

Narendra said: (Dec 14, 2010)
Thanks for the shortcut.

Lopa said: (May 18, 2011)
Thanks rajesh for this method.

Kiran said: (Jul 10, 2011)
Let the num is 3. Then square of 3 is 9 so 9/5 remainder is 4.

Neha Nagar said: (Mar 12, 2012)
For this kind of question consider any no. Suppose 13/5 gives remainder 2 then the square of 13 means 169 when divided by 169 gives remainder 4.

Sanju said: (Mar 21, 2012)
Thanks Neha for easy shortcut.

Amit said: (Jun 27, 2012)
x/5 = 3. Square of (x/5)/5 = 9/5 = 4.

Naina Sanghvi said: (Mar 21, 2013)
Number is 5k+3. This number when divided by 5 will give the remainder as: 5k/5 = 0+3/5 = 3 i.e; 0+3 = 3. Now (3)^2 = 9. Remainder when 9/5 = 4.

Nil.dhongde said: (Apr 10, 2013)

@Rajesh rao method is very wrong. It doesn't follow the rules everywhere. This method is like hit and try. The original universal method is given itself in problem. Wanna check it out if Mr Rajesh rao's method is right or wrong. Try this. So here is similar problem for those, who used to use other shortcuts method.

if certain number is divided by 7 gives 6 as remainder. What will be the remainder if square of the same number is divided by 7?

Balaji Shinde said: (Jun 10, 2013)
5+3 = 8. So square of 8 is 64. If 64/5 remainder will be 4.

Udaya Santhi said: (Aug 20, 2013)
The number taken as n. n = 5q+3. The square of the number is nn=(5q+3)^2. That number is divisible by 5. Therefore, [(5q+3)^2]/5={[(5q)^2/5]+[2(5q)(3)/5]}+[9/5]. The flower bracket whole number is divisible by 5. But 9/5 = remainder is 4.

Bharathi said: (Feb 21, 2014)
For example x = 13. We will divide 13/5 we get reminder as =3. The square of the 13 has 169. 169 is divided by 5 we get reminder as 4. So answer = 4.

Ankita said: (Sep 4, 2014)
If we subtract the remainder by number i.e. x - 3 and divide it by 5 we will get zero. Therefore (x - 3)/5 = 0. x = 3. Now 3^2 = 9. & 9/5 the remainder will be 4.

Purushothaman said: (Nov 20, 2014)
Exclusive me, I have little doubt how could come to 30 k please explain me.

Jeevitha said: (May 4, 2015)
Let the number be x. x = 5k+3. Let us take k = 1. Then x = 5(1)+3. x = 8. So, square of 8 = 64. When 64 is divided by 5. Remainder is 4. Therefore, answer is 4.

Narendra said: (Jun 21, 2015)
As take remainder that is 3 square it 9 divide it by 5 answer will be 4.

Aparna said: (Jun 29, 2015)
How could 30k has come in this answer please anyone explain me.

Reshma said: (Jul 25, 2015)
Difference - remainder = question - 1. 5-3 = x-1. x = 2+1 = 3. 3^2 = 9. 9/5 =4.

Sukesh said: (Sep 25, 2015)
Consider the two reminders first we got 3 before squaring the number. After squaring and dividing we got 5 as reminder. So square the 1st reminder 3^2=9. Then, 9/5=4 is the reminder.

Sayali said: (Oct 2, 2015)

Easiest way. We have ask square of the no: So 3 square is 9. 9/5 remainder is 4. 4 is the answer.

Apply this method to sum no 41.

Neha Yadav said: (Feb 11, 2016)
In the above equation 30K come by algebra formula i.e. (a+b)^2 = a^2+2ab+b^2.

Shriram Deshmukh said: (Aug 5, 2016)
Dividing number by 5 its means multi of 5. (5 * 1 + 3) = 8--> 64/5=> rem 4. (5 * 2 + 3) = 13--> 169/5=>rem 4. (5 * 3 + 3) = 18--> 324/5=>rem 4. And so on.

Raja Virat said: (Nov 19, 2016)
Let the number be 23. When 23 is divided by 5 we get remainder as 3, Then, square of the number = 23 * 23 = 529. So, 529/5 = 4.

Kums Kutty said: (Jan 20, 2017)
In problem x is divisable by 5 then the remainder is 3 so we have X/5=3 then find x value X = 5 * 3 = 15. In problem, they mentioned square of X is divisible by 5 then what is the remainder. So X value is 15 then it's square is 225 now we divide it by 5. 225/5 = 45, 45/5 = 9, 9/5 = 4 as a remainder.

Ashi said: (Jan 27, 2017)
@Nil.Dhongde. The answer is 1.

Bhuiyanislam said: (Jun 5, 2017)
Difference - remainder = question - 1. 5 - 3 = x - 1. x = 2 + 1 = 3. 3^2 = 9. 9/5 = 4.

Mohammed said: (Jan 6, 2018)
How could come 30 k in above equation?

Bhavani said: (Feb 21, 2018)

@Rajesh Rao.

You explained in a easy way Thank you !

IKRAMUL said: (Aug 4, 2018)
The square of this no means 3 *3=9. And 9/5 rem is for, Also let a no which divides by 5 rem is 3. Where 8/5 rem is 3, The square of this no is 64, 64/5 we get 4 is a rem.

Bhuvana Ram said: (Jun 24, 2019)
Formula:(Divisor * Quotient) + remainder = Dividend. So, (5Q)+3=D ----> (1) D^2%5=R -----> (2) Now we substitute equation(1) in (2). ((5Q)+3)^2%5 = R Assume Q = 1, (5+3)^2%5 = R. (8)^2%5 = R, 64%5 = R, 4 = R.

Radha Gayathri said: (Jun 29, 2020)
Formula: dividend = divisor * quotient + remainder. Divisor=5, reamainder=3. 5q+3. (5q+3)^2/5. Assume q as 1, (5+3)^2/5, (8)^2/5, 64/5. And the remainder is 4.

Karthik Pyati said: (Jul 3, 2020)
1step: to add 5+3=8 den divide by 5, will give remainder as 3, then square the remainder number 3 i.e(3^2)=9, when dividing the no 5 & the remainder will be 4.

Pema said: (Oct 2, 2020)
Thank you @Neha Nagar.

Kamila Banu said: (Mar 31, 2021)
= 3 * 3 = 9. = 9 - 5 = 4.

Pavishka said: (Jun 11, 2021)
We assume the nearest value + reminder. i.e 5 + 3 = 8 8/5 = 1 (reminder=3) And square of 8 is 64 64/5 = 12 The reminder is 4 so, ans = 4.