Can you Please explain the answer that I received of 2469? It is the correct answer but I do not understand how to show the work. Thank you
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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.
sort of answered below - see links
write the 2-digit number that mathes the clues.my number has a tens digits that is 8 more than the ones digit.zero is not one of my digits.
To solve this problem and find a set of four different digits that is not divisible by 7, you need to follow these steps:
1. Write down all possible four-digit numbers that can be formed using the nine given digits, 1, 2, 3, 4, 5, 6, 7, 8, and 9.
2. Start by considering the digits 1238. To find out if this set of digits can form a number divisible by 7, you can use the divisibility rule for 7, which states that you can remove the last digit, double it, and subtract it from the remaining number. If the result is divisible by 7, then the original number is divisible by 7.
For the digit set 1238, removing the last digit gives 123. Doubling the last digit (8) gives 16. Subtracting 16 from 123 gives 107. Since 107 is not divisible by 7, the set of digits 1238 cannot form a number divisible by 7.
3. Repeat the same process for the digits 1389. Removing the last digit gives 138. Doubling the last digit (9) gives 18. Subtracting 18 from 138 gives 120. Since 120 is not divisible by 7, the set of digits 1389 cannot form a number divisible by 7.
4. Continue by analyzing the remaining digit sets until you find one that does not form a number divisible by 7.
Let's move on to the next set of digits:
The digits 2469 can be arranged in various ways to form four-digit numbers. To find the smallest four-digit number that is not divisible by 7, you can try all possible permutations.
The possible arrangements of the digits 2469 are:
- 2469
- 2496
- 2649
- 2694
- 2946
- 2964
- 4269
- 4296
- 4629
- 4692
- 4926
- 4962
- 6249
- 6294
- 6429
- 6492
- 6924
- 6942
- 9246
- 9264
- 9426
- 9462
To check if any of these numbers are divisible by 7, you can use the same divisibility rule mentioned earlier. However, it would be time-consuming to manually check all of them.
Instead, you can use a calculator or a programming language to compute the remainder of each number when divided by 7. If the remainder is equal to zero, then the number is divisible by 7. If the remainder is not zero, then the number is not divisible by 7.
After checking all the possible permutations, you will find that none of the numbers formed by the digits 2469 is divisible by 7. Therefore, the correct answer is 2469.
I hope this explanation helps you understand how to approach this problem and verify if a number is divisible by 7.