Find the sum of all prime numbers between 1 and 100 that are

simultaneously 1 greater than a multiple of 4 and 1 less than a
multiple of 5.

(a) 118
(b) 137
(c) 158
(d) 187
(e) 245

The answer is D right?

No, it isn't. Try again

Some numbers that qualify are 9, 29 and 49. See if you can see a pattern.

To find the sum of all prime numbers between 1 and 100 that are simultaneously 1 greater than a multiple of 4 and 1 less than a multiple of 5, we need to follow these steps:

1. Identify the prime numbers between 1 and 100.
2. Among the prime numbers, identify the ones that are 1 greater than a multiple of 4 (4n + 1) and 1 less than a multiple of 5 (5m - 1).
3. Add up these prime numbers.

Let's go through each step:

1. Identifying the prime numbers between 1 and 100:
Prime numbers are numbers that are only divisible by 1 and themselves. Using this definition, we can list the prime numbers between 1 and 100: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97.

2. Identifying the prime numbers that meet the given conditions:
We need to find prime numbers that are 1 greater than a multiple of 4 and 1 less than a multiple of 5. By checking each prime number from step 1, we can identify the following primes that meet the conditions: 5, 13, 17, 29, 37, 41, 53, 61, 73, 89.

3. Adding up the prime numbers from step 2:
The sum of these prime numbers is 5 + 13 + 17 + 29 + 37 + 41 + 53 + 61 + 73 + 89 = 418.

Now, looking at the possible answer choices:
(a) 118
(b) 137
(c) 158
(d) 187
(e) 245

The calculated sum of the prime numbers is 418, which does not match any of the answer choices. Therefore, the correct answer is none of the given answer choices.