Need Answer to the Following Please:
Using the 9 digits, 1, 2, 3, 4, 5, 6,7, 8 and 9 you can arrange four different digits to form a four-digit number that is NOT divisible by 7. The digits 1238 cannot be arranged to create a four-digit number that is divisible by 7. The digits 1389 also cannot be arranged to form a four-digit number that is divisible by 7. Find one additional set (not 1238 or 1389) of four different digits that is not divisible by 7. Provide the digits to form the smallest four digit value.
Please explain. Thank You
how about 1245 or 3489, or ...
pick any four digits. If the number is divisible by 7, raise a digit by less than 7, and there will now be a nonzero remainder.
To find another set of four digits that is not divisible by 7, we can use a method of trial and error.
We know that the sets of digits 1238 and 1389 cannot be arranged to form four-digit numbers that are divisible by 7.
First, let's consider the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9. From this set, we need to choose four different digits to form the smallest possible four-digit number.
To determine if a number is divisible by 7, we can use the divisibility rule for 7, which states that if subtracting twice the units digit from the remaining truncated number is divisible by 7, then the original number is also divisible by 7.
Let's start by choosing the digit 9 as our first digit. We now have 9 _ _ _. For the remaining three digits, we have the following options:
1. We cannot use the digits 1, 2, or 3 because the sets 1238 and 1389 are not divisible by 7.
2. If we choose the number 4 as the second digit, we would have 9 4 _ _. For the remaining two digits, we have 5, 6, 7, and 8 to choose from.
Now, let's check if the numbers formed by choosing the remaining two digits are divisible by 7:
- If we choose 5 as the third digit, we would have 9 4 5 _. The only remaining digit is 6.
- If we choose 6 as the third digit, we would have 9 4 6 _. The only remaining digit is 5.
- If we choose 7 as the third digit, we would have 9 4 7 _. The only remaining digit is 8.
- If we choose 8 as the third digit, we would have 9 4 8 _. The only remaining digit is 7.
Now, let's check if the formed numbers are divisible by 7:
- For the number 9456, if we subtract twice the units digit (2 * 6 = 12) from the truncated number (945), we get 933. Since 933 is divisible by 7, 9456 is also divisible by 7. Therefore, we cannot use this combination.
- For the number 9465, if we subtract twice the units digit (2 * 5 = 10) from the truncated number (946), we get 926. Since 926 is not divisible by 7, 9465 is also not divisible by 7. Therefore, this is a valid combination.
Thus, the smallest four-digit number that meets the given conditions is 9465.