find the s tum of 3 prime number who sum 100
Answers
Step-by-step explanation:
1. As shown by Kurt Mager one of the three digits must be 2
2. To get 100, the sum of last digit of the remaining two digits must
be “8” i.e. (1,7), (2,6), (3,5), (4,4) (9,9) or inverse of these pairs
(7,1), (6,2), (5,3)
3. Two-digit number ending with 2 or 6 can’t be a prime number hence (2,6)
can be rejected.
4. Two-digit number ending with 5 can’t be a prime number hence (3,5) can
be rejected
5. Two-digit number ending with (4,4) can’t be a prime number hence (4,4)
can be rejected.
Thus, valid options for the last digit of a two-digit number are (1,7), (9,9) and (7,1)
Two digit Prime numbers ending with 1 are 11, 31, 41, 61, 71
Two-digit prime numbers ending with 7 are 17, 37, 47, 67,97
Hence valid pair are (31, 67), (37,61)
(9,9)—first prime number ending with 9 is 19 and hence second number ending with 9
must be 79 e.g., 2 + 19 + 79
Answer:
2 + 31 + 67
2 + 37 + 61
2 + 19 + 70