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Select all the digits that make this statement true.41 573 03? is divisible by 6.0948Submit

Question

Select all the digits that make this statement true.

41 573 03? is divisible by 6.0948.

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Solution

To determine if a number is divisible by 6, it must meet two conditions: it must be divisible by 2 (i.e., it is an even number) and it must be divisible by 3 (i.e., the sum of its digits is divisible by 3).

  1. For a number to be divisible by 2, its last digit must be even (0, 2, 4, 6, or 8).

  2. For a number to be divisible by 3, the sum of its digits must be divisible by 3. The sum of the digits in the number 4157303? is 23 + ?.

Let's find the possible values for ?:

If ? = 0, the sum of the digits is 23 which is not divisible by 3. If ? = 1, the sum of the digits is 24 which is divisible by 3. But 41573031 is not an even number. If ? = 2, the sum of the digits is 25 which is not divisible by 3. If ? = 3, the sum of the digits is 26 which is not divisible by 3. If ? = 4, the sum of the digits is 27 which is divisible by 3. But 41573034 is not an even number. If ? = 5, the sum of the digits is 28 which is not divisible by 3. If ? = 6, the sum of the digits is 29 which is not divisible by 3. If ? = 7, the sum of the digits is 30 which is divisible by 3. But 41573037 is not an even number. If ? = 8, the sum of the digits is 31 which is not divisible by 3. If ? = 9, the sum of the digits is 32 which is not divisible by 3.

Therefore, there are no digits that can make the statement "41 573 03? is divisible by 6" true.

This problem has been solved

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