Question

Write one digit on each side of 23 to make a four digit multiple of 72. How many different solutions does this problem have?

Answer 1

Given: 23 and 72 as two numbers.

To find: Write one digit on each side of 23 to make a four digit multiple of 72.

Solution:

• So we can  check if the nine, 4 digit numbers that result from the given question are multiples of 72:

• So these are:

         1231 , 2232 , 3232 , till  9232

• But we know that 72 is even,so the answer should also result in even, so we can delete or terminate the odd cases, leaving just :

          2232 ,  4234 ,  6236 , 8234

• Now only have 4 numbers to check. only the first of these is a multiple of 3, and hence 2232 is the only answer.

Answer:

So there is only one solution and it is 2232.