Question

The values of remainder r ,when a positive integer a is divided by 3,are 0 and 1 only. Is this statement true or false? Justify your answer.
(Class 10 Maths Sample Question Paper)

Answer 1

SOLUTION:
The given statement the values of remainder r ,when a positive integer a is divided by 3,are 0 and 1 only is FALSE. According to Euclid's division Lemma, a = b q+ r

Here, b = 3

a = 3 q + r,

Where 0 ≤ r < 3 and r is an integer.

Therefore , the values of r can be zero ( 0 ) , one ( 1 ) or two ( 2 ).

HOPE THIS WILL HELP YOU....

Answer 2

Hey there !!

Let a be the positive integer and b = 3 be the divisor then there exist ,

a = bq + r , where 0≤r< b ...... ( 1 )

Here ,

statement says that -
"When a which is an positive integer divided by three then remainder will be 0 or 1 only"

But we know from ( 1 ) that

remainder can be , ➱ 0 , 1 , 2

Hence this statement is proven to be false

Hope this would help you !!