The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.Consider the following statements:1. The sum of the two digits of the number can be determined only if the product of the two digits is known.2. The difference between the two digits of the number can be determined.Which of the above statements is/are correct?
Question
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.Consider the following statements:1. The sum of the two digits of the number can be determined only if the product of the two digits is known.2. The difference between the two digits of the number can be determined.Which of the above statements is/are correct?
Solution
Let's break down the problem:
A 2-digit number can be expressed as 10x + y, where x is the tens digit and y is the units digit. When the digits are reversed, the number becomes 10y + x.
According to the problem, the difference between the original number and the reversed number is 54. So, we can write the equation:
10x + y - (10y + x) = 54 9x - 9y = 54 x - y = 6
Now, let's analyze the statements:
- The sum of the two digits of the number can be determined only if the product of the two digits is known.
This statement is incorrect. The sum of the digits can be determined without knowing the product of the digits. For example, if x = 7 and y = 1, the sum of the digits is 8, regardless of the product.
- The difference between the two digits of the number can be determined.
This statement is correct. From the equation x - y = 6, we can determine that the difference between the two digits is 6.
So, only statement 2 is correct.
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