I am a number between 60 and a 100. My ones digit is 2 less than my tens digit. I am a prime number. What am I? Explain.
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What is your answer?
97
Right.
It is 74
97
To find the prime number that satisfies the given conditions, we can follow these steps:
Step 1: Determine the tens digit range
Since the number is between 60 and 100, the tens digit can be 6, 7, 8, or 9.
Step 2: Calculate the ones digit
The ones digit is 2 less than the tens digit. Therefore, we need to subtract 2 from each possible tens digit to get the corresponding ones digit:
For 6, ones digit = 6 - 2 = 4.
For 7, ones digit = 7 - 2 = 5.
For 8, ones digit = 8 - 2 = 6.
For 9, ones digit = 9 - 2 = 7.
Step 3: Combine the tens and ones digit
Now, we have four possible numbers: 64, 75, 86, and 97.
Step 4: Check for prime numbers
To determine if the numbers are prime, we need to see if any of them are divisible by any number other than 1 and itself.
Starting with 64: We can eliminate this number since it is divisible by 2 (32 x 2 = 64) and therefore not a prime number.
Next, 75: We can eliminate this number as well since it is divisible by 3 (25 x 3 = 75) and, therefore, not prime.
Continuing with 86: We can eliminate this number too, as it is divisible by 2 (43 x 2 = 86) and, thus, not prime.
Lastly, 97: This is a prime number since it is only divisible by 1 and itself. So, the number you are looking for is 97.
In conclusion, the number that satisfies the given conditions (between 60 and 100, ones digit is 2 less than tens digit, and is a prime number) is 97.