Question

Let n be the number of 4-digit numbers of the form xyz which satisfy x=y+z and m be the number of 4 -digit numbers of the form xyz which satisfy z=x+y, then what is difference between m and n?

Answer 1

To find the difference between m and n, we need to calculate the number of possibilities that satisfy the given conditions for each case. By evaluating the range of values for x, y, and z, and substituting them into the given equations, we can determine the number of valid 4-digit numbers for n and m. Then, subtract the total number of possibilities for n from the total number of possibilities for m to find the difference.

Step-by-step explanation:

In order to find the difference between m and n, we need to first find the values of m and n. Let's break it down step by step:

1. For n, the number of 4-digit numbers of the form xyz where x=y+z, we have x ranging from 1 to 9 (since x cannot be 0 for a 4-digit number), y ranging from 0 to 9, and z = x - y.
2. Similarly, for m, the number of 4-digit numbers of the form xyz where z=x+y, we have x ranging from 1 to 9, y ranging from 0 to 9, and z = x + y.
3. By substituting the values of x, y, and z, we can find the number of possibilities for each case and calculate the difference between m and n.
4. For example, let's take the case where x=1, y=0, and z=x-y=1-0=1. This satisfies the condition x=y+z, so it is a valid possibility for n. Similarly, when x=1, y=0, and z=x+y=1+0=1, it satisfies the condition z=x+y and is a valid possibility for m.
5. Repeat this process for all possible values of x, y, and z and calculate the number of valid possibilities for each case.
6. Finally, find the difference between the total number of possibilities for m and n to get the answer.