Question

1 . In the equation below, a, b, q, r are integers, 0≤r<b, a is a multiple of 3 and b=9. a=b q+r Which of the following forms represent a? ​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

In the equation below, a, b, r are integers, O≤r<b, a is a multiple of 3 and b=9.

a=bq+r

Which of the following forms represent a

Option 1 : Only 9q and 9q+3, as only these forms when divided by 3 gives r=0.

Option 2: Only 9q+1 and 9q+4, as only these forms when divided by 3 gives r = 1.

Option 3: Only 9q,9q+3, and 9q+6. as only these forms when divided by 3 gives r=0.

Option 4: Only 9q+1, 9q+4, and 9q+7, as only these forms when divided by 3 gives r=1.

EVALUATION

Here it is given that a, b, r are integers, 0≤r<b, a is a multiple of 3 and b=9.

Since a is a multiple of 3

Let a = 3m

Thus a=bq+r gives

3m = 9q + r - - - - - - (1)

Since 0 ≤ r < b and b = 9

We have 0 ≤ r < 9

So r = 0 , 1 , 2 , 3 ,..., 8

From Equation 1 we get

r = 0 , 3 , 6

So a is of the form 9q,9q+3, and 9q+6

Hence Only 9q,9q+3, and 9q+6. as only these forms when divided by 3 gives r = 0

FINAL ANSWER

Hence the correct option is

Option 3: Only 9q,9q+3, and 9q+6. as only these forms when divided by 3 gives r=0

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Answer 2

Step-by-step explanation:

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