# Aptitude - Numbers - Discussion

Discussion Forum : Numbers - General Questions (Q.No. 31)
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 ?
0
1
2
4
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.

Discussion:
36 comments Page 1 of 4.

Jaisree said:   1 year ago
We can square the reminder and divide it by 5.
3^3 = 9.
9/5 = 4 (rem).
(3)

Pavishka said:   2 years ago
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.
(1)

Kamila Banu said:   2 years ago
= 3 * 3 = 9.
= 9 - 5 = 4.

Pema said:   2 years ago
Thank you @Neha Nagar.

Karthik pyati said:   3 years ago
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.

Radha gayathri said:   3 years ago
Formula: dividend = divisor * quotient + remainder.
Divisor=5, reamainder=3.
5*q+3.
(5*q+3)^2/5.
Assume q as 1,
(5+3)^2/5,
(8)^2/5,
64/5.

And the remainder is 4.

Bhuvana ram said:   4 years ago
Formula:(Divisor * Quotient) + remainder = Dividend.

So, (5*Q)+3=D ----> (1)
D^2%5=R -----> (2)

Now we substitute equation(1) in (2).

((5*Q)+3)^2%5 = R
Assume Q = 1,
(5+3)^2%5 = R.
(8)^2%5 = R,
64%5 = R,
4 = R.

IKRAMUL said:   5 years ago
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.
(1)

Bhavani said:   5 years ago
@Rajesh Rao.

You explained in a easy way Thank you !

Mohammed said:   5 years ago
How could come 30 k in above equation?