Question

make two 4 digit numbers using each of the digits 1,2,3,4 and 5 such that the numbers made are divisible by 132​

Answer 1

Step-by-step explanation:

All multiples of 4 end in an even digit. (even digit in the units)

If the unit digit is 0, 4, or 8, the next to last digit (the digit in the tens) must be even. If the unit digit is 2 or 6, the tens digit shall be odd.

So, any of these five digits can be in the tens, and for each digit in the tens, there is only one possible digit in the units. The five possible ending combinations are 12, 24, 32, 44, 52.

Then, whatever goes in the hundreds and tousands is independent, and you have five digits to choose. So the answer is 5×5×5=125

A list of all of them:

1112 1124 1132 1144 1152

1212 1224 1232 1244 1252

1312 1324 1332 1344 1352

1412 1424 1432 1444 1452

1512 1524 1532 1544 1552

2112 2124 2132 2144 2152

2212 2224 2232 2244 2252

2312 2324 2332 2344 2352

2412 2424 2432 2444 2452

2512 2524 2532 2544 2552

3112 3124 3132 3144 3152

3212 3224 3232 3244 3252

3312 3324 3332 3344 3352

3412 3424 3432 3444 3452

3512 3524 3532 3544 3552

4112 4124 4132 4144 4152

4212 4224 4232 4244 4252

4312 4324 4332 4344 4352

4412 4424 4432 4444 4452

4512 4524 4532 4544 4552

5112 5124 5132 5144 5152

5212 5224 5232 5244 5252

5312 5324 5332 5344 5352

5412 5424 5432 5444 5452

5512 5524 5532 5544 5552

Whit no repeating numbers:

Still the two last digits must show it is divisible by 4. But we must discard 44. So we have four different endings.

Whatever ending we choose, we have used two digits of the five available. So we have only 3 possible choices for the hundreds, and 2 possible choices for the thousands.

So the answer is 4×3×2=24