I am a 2-digit number with a 1-digit decimal. I am bigger than 54 but smaller than 56. 2 of my digits are even. When you divide my whole number by the digit in my decimal place, the answer has no remainder. What are the biggest and smallest numbers I could be?
can't figure this one out
To find the biggest and smallest numbers that meet the given conditions, we can use a step-by-step approach.
Step 1: Identify the range of possible values for the whole number part.
- The whole number must be bigger than 54 but smaller than 56.
- Therefore, it can be either 55 or 54.
Step 2: Determine the range of possible values for the decimal digit.
- The decimal digit must be a 1-digit even number.
- The possible values are 0, 2, 4, 6, or 8.
Step 3: Combine the whole number and decimal digit to find all possible numbers.
- For the whole number 55, the decimal digit can be 0, 2, 4, 6, or 8. This yields the numbers 55.0, 55.2, 55.4, 55.6, and 55.8.
- For the whole number 54, the decimal digit can also be 0, 2, 4, 6, or 8. This gives the numbers 54.0, 54.2, 54.4, 54.6, and 54.8.
Therefore, the biggest number that meets the given conditions is 55.8, while the smallest number is 54.0.
To solve this problem, let's break it down step by step:
Step 1: Find the range of possible whole numbers.
- We know that the number is bigger than 54, so the smallest possible whole number is 55.
- We also know that the number is smaller than 56, so the largest possible whole number is 55.
Step 2: Determine the possible digits in the decimal place.
- Since the number is a 2-digit number, the decimal digit can only be one of {0, 2, 4, 6, 8} because even digits are required.
Step 3: Find the biggest and smallest numbers by combining the whole number and decimal.
- The biggest number occurs when we take the largest possible whole number and the largest possible decimal digit.
- The largest whole number is 55, and the largest decimal digit is 8. So the biggest number is 55.8.
- The smallest number occurs when we take the smallest possible whole number and the smallest possible decimal digit.
- The smallest whole number is also 55, and the smallest decimal digit is 0. So the smallest number is 55.0.
Therefore, the biggest number you could be is 55.8, and the smallest number you could be is 55.0.
Since the 54 < n < 56, and has 2 even digits, it must be 54.x where x is even and divides 54:
54.6, 54.2