Question

Find the largest 3 digit number,with no two digits the same and with its digits in ascending order,which when multiplied by 5 has its digits in descending order?

Answer 1

The largest 3 digit number with no two digits the same and with its digits in ascending order is 987, and when multiplied by 5, it has its digits in descending order.

Step-by-step explanation:

To find the largest 3 digit number with no two digits the same and with its digits in ascending order, we need to start with the highest digit possible which is 9. Then we move to the next highest digit which is 8, and finally the smallest digit which is 7. So the largest 3 digit number with no two digits the same and in ascending order is 987.

To check if this number, 987, when multiplied by 5 has its digits in descending order, we multiply it by 5: 987 * 5 = 4935. The digits in 4935 are indeed in descending order, so 987 is the largest 3 digit number that satisfies both conditions.

Answer 2

To represent the number in ascending order, we can use the variables x,y and z to represent separate digits. IN this case, in ascending order, the formula is x + 10 y + 100 z. On the other hand, the descending order is z + 10y + 100x. The expression then becomes (x + 10 y + 100 z)*5 = z + 10y + 100x. The other functions are x and z should be greater than 1 to 9 while y allows zero.