Question

If 21y6 is a multiple of 3, where y is a digit, what might be the values of y ?​

Answer 1

$\bf\pink{QuestioN:-}$

If 21y6 is a multiple of 3, where y is a digit, what might be the values of y ?​

$\bf\blue{AnsweR:-}$

Solution :-

According to the given condition,

• 21y6 is a number, which is a multiple of 3.

As we know,

• The sum of the digits of the multiples of 3 will be

• 3 , 6 or 9.

So here,

• 2 + 1 + y + 6 must be equal to 3, 6 or 9.

• 2 + 1 + y + 6 = 9 + y

If this number is a multiple of 3 , then

• 9 + y = 3 , 6 or 9.

• 9 is already a multiple of 3.

• So y = 3 , 6 or 9.

Verification :-

1st Case :-

If y = 3

2136 will be the number.

2 + 1 + 3 + 6 = 12

1 + 2 = 3

2136 ÷ 3 = 712

Hence it is a multiple of 3.

Verified !!

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2nd Case :-

If y = 6

2166 will be the number.

2 + 1 + 6 + 6 = 15

1 + 5 = 6

2166 ÷ 3 = 722

Hence it is a multiple of 3.

Verified !!

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3rd Case :-

If y = 9

2196 will be the number .

2 + 1 + 9 + 6 = 18

1 + 8 = 9

2196 ÷ 3 = 732

Hence it is a multiple of 3 .

Verified !!

☆-----------------------------------------------☆

So the required answer for your question is ,

$\huge{\boxed{\boxed{\bf{\bigstar{3,6\:or\:9\bigstar}}}}}$

All Done !!☺