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If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:
- a)0
- b)1
- c)2
- d)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
If the number 517*324 is completely divisible by 3, then the smallest ...
Sum of digits = (5 + 1 + 7 + x + 3 + 2 + 4) = (22 + x),
which must be divisible by 3.
x = 2.
Most Upvoted Answer
If the number 517*324 is completely divisible by 3, then the smallest ...
Solution:
Divisibility Rule of 3: A number is divisible by 3, if the sum of its digits is a multiple of 3.
Let's find the sum of digits of 517*324:
5 + 1 + 7 + * + 3 + 2 + 4 = 22 + *
For the number to be divisible by 3, the sum of its digits must be a multiple of 3.
If the sum of digits is 1, 4, 7 or any other number not divisible by 3, then the number is not divisible by 3.
If the sum of digits is 3, 6, 9 or any other number divisible by 3, then the number is divisible by 3.
To make the sum of digits a multiple of 3, we need to replace * with a number such that the sum of digits is a multiple of 3.
Let's try replacing * with 0, 1, 2 and check which one gives a sum of digits that is a multiple of 3.
- If * = 0, then the sum of digits = 22 + 0 = 22, which is not divisible by 3.
- If * = 1, then the sum of digits = 22 + 1 = 23, which is not divisible by 3.
- If * = 2, then the sum of digits = 22 + 2 = 24, which is divisible by 3.
Therefore, the smallest whole number in the place of * that makes the number divisible by 3 is 2.
Hence, option C is the correct answer.
Divisibility Rule of 3: A number is divisible by 3, if the sum of its digits is a multiple of 3.
Let's find the sum of digits of 517*324:
5 + 1 + 7 + * + 3 + 2 + 4 = 22 + *
For the number to be divisible by 3, the sum of its digits must be a multiple of 3.
If the sum of digits is 1, 4, 7 or any other number not divisible by 3, then the number is not divisible by 3.
If the sum of digits is 3, 6, 9 or any other number divisible by 3, then the number is divisible by 3.
To make the sum of digits a multiple of 3, we need to replace * with a number such that the sum of digits is a multiple of 3.
Let's try replacing * with 0, 1, 2 and check which one gives a sum of digits that is a multiple of 3.
- If * = 0, then the sum of digits = 22 + 0 = 22, which is not divisible by 3.
- If * = 1, then the sum of digits = 22 + 1 = 23, which is not divisible by 3.
- If * = 2, then the sum of digits = 22 + 2 = 24, which is divisible by 3.
Therefore, the smallest whole number in the place of * that makes the number divisible by 3 is 2.
Hence, option C is the correct answer.
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If the number 517*324 is completely divisible by 3, then the smallest whole number in the place of * will be:a)0b)1c)2d)None of theseCorrect answer is option 'C'. Can you explain this answer?
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