Joe says that the product of a 4 digit number and a 1 digit number is always a 4 digit number does joe's statement makes sense?

No because thw product of 9 and anything above 1112 would be 10,008+

No, what Joe said isn't necessarily true. Though it is common that the product will be a 4 digit number, because you can use any number, like a large 4 digit number like 9999 or a large 1 digit number like 9, that isn't true. For instance: "9999 x 9" is 89991 which is 5 digits instead of 4 because "9999" is the biggest 4 digit number and "9" is the biggest "1" digit number.

176521221 divisible by 9 but not by 11

149235678 divisible by 9 but not by 11

Step-by-step explanation:

There are rules that can be used to determine if a number is divisible by other. We will use the following:

- A number is divisible by 9, if the sum of its digits is divisible by 9.

- A number is divisible by 11, if the alternating sum of the digits read from left to right is divisible by 9.

Let's apply this rules to the given numbers...

For 176521221:

1 + 7 + 6 + 5 + 2 + 1 + 2 + 2 + 1 = 27, and  27 divisible by 9 => 176521221 divisible by 9 1 - 7 + 6 - 5 + 2 - 1 + 2 - 2 + 1 = -3, and -3 not divisible by 11 => 176521221 not divisible by  11

For 149235678 :

1 + 4 + 9 + 2 + 3 + 5 + 6 + 7 + 8  = 45, and 45 divisible by 9 => 149235678 divisible by 91 - 4 + 9 - 2 + 3 - 5 + 6 - 7 + 8  = 9, and 9 not divisible by 11 => 149235678 not divisible by  11