A positive two-digit number is such that the product of the digits is 24.When the digits are reversed the number formed is greater than the original number by 18.Find the number.
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To find the number, start by listing all possible two-digit numbers whose digits multiply to 24. We can do this by finding all pairs of factors of 24. The factors of 24 are:
1 × 24
2 × 12
3 × 8
4 × 6
Now we need to check if reversing the digits of each number results in a number that is 18 greater than the original number. We can do this by subtracting the original number from the reversed number and checking if the difference is 18.
Let's go through each possibility:
1. For the number 12:
Reversed number: 21
21 - 12 = 9 (not 18)
2. For the number 24:
Reversed number: 42
42 - 24 = 18 (it matches!)
So 24 is a possible number.
3. For the number 38:
Reversed number: 83
83 - 38 = 45 (not 18)
4. For the number 46:
Reversed number: 64
64 - 46 = 18 (it matches!)
So 46 is a possible number.
Now we have found two possible numbers: 24 and 46. However, we need to find the positive two-digit number, which means we must eliminate any numbers that have a zero as one of the digits.
Since 24 is the only number without a zero in its digits, the answer is 24.