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.
Will you Please explain the answer also. Thank You
what's to explain? The number is not divisible by 7.
How about 6789 or 5678 or 1579?
Oops. I see I did not read carefully; no arrangement is allowed to be divisible by 7. In that case, the only one I can find is
2469
To find a set of four different digits that is not divisible by 7, we need to consider the divisibility rule for 7. According to the rule, a number is divisible by 7 if and only if the difference between twice the units digit and the rest of the number is divisible by 7.
Let's use this rule to determine which set of digits is not divisible by 7.
Starting with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9, we can create all possible four-digit numbers by selecting four digits and arranging them.
Now, we need to check if each four-digit number we create is divisible by 7 or not. We can check this by applying the divisibility rule for 7 as mentioned above.
For the digits 1238 and 1389, the four-digit numbers cannot be arranged in such a way that they are divisible by 7.
To find another set of four different digits that is not divisible by 7, we can go through the remaining numbers.
1. Let's consider the set of digits 1245. We can create four-digit numbers by arranging these digits in different orders - 1245, 1254, 1425, 1452, 1524, 1542, 2145, 2154, 2415, 2451, 2514, 2541, 4125, 4152, 4215, 4251, 4512, 4521, 5124, 5142, 5214, 5241, 5412, 5421.
2. Now, let's apply the divisibility rule for 7 to each of these four-digit numbers.
- The difference between twice the units digit (2 x 5 = 10) and the rest of the digits is:
- For 1245: 124 - 10 = 114
- For 1254: 125 - 10 = 115
- For 1425: 142 - 10 = 132
- For 1452: 145 - 10 = 135
- For 1524: 152 - 10 = 142
- For 1542: 154 - 10 = 144
- For 2145: 214 - 10 = 204
- For 2154: 215 - 10 = 205
- For 2415: 241 - 10 = 231
- For 2451: 245 - 10 = 235
- For 2514: 251 - 10 = 241
- For 2541: 254 - 10 = 244
- For 4125: 412 - 10 = 402
- For 4152: 415 - 10 = 405
- For 4215: 421 - 10 = 411
- For 4251: 425 - 10 = 415
- For 4512: 451 - 10 = 441
- For 4521: 452 - 10 = 442
- For 5124: 512 - 10 = 502
- For 5142: 514 - 10 = 504
- For 5214: 521 - 10 = 511
- For 5241: 524 - 10 = 514
- For 5412: 541 - 10 = 531
- For 5421: 542 - 10 = 532
By checking these differences, we can see that none of these four-digit numbers have a difference that is divisible by 7. Therefore, all these numbers formed with the digits 1245 are not divisible by 7.
To provide the digits to form the smallest four-digit value, we can consider the lowest arrangement, which is 1245.