# 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 ?

Answer: Option

Explanation:

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

*x* = 5k + 3

*x*^{2} = (5k + 3)^{2}

= (25*k*^{2} + 30*k* + 9)

= 5(5*k*^{2} + 6*k* + 1) + 4

On dividing *x*^{2} 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).

3^3 = 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.

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.

= 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.

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.

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.

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 !

You explained in a easy way Thank you !

Mohammed said:
5 years ago

How could come 30 k in above equation?

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