There are 5 prime numbers.
Sum of them is 100.
Product of them is a number in form of ABCABC
Find A+B+C.
Solution to the Problem:
Here is Davit Banana's solution:If we divide ABCABC by ABC, the result is (always) 1001.
If we factorize 1001 to prime numbers, we find 7, 11 and 13.
So, 3 of the numbers are 7, 11 and 13
The other 2 numbers’ sum is 100-7-11-13 = 69
Since 69 is odd, one of the remaining numbers has to be even (and the other, odd).
The only even prime number is 2, so the fourth number is 2.
The fifth number is 69-2 = 67.
So, ABC is 2x67 = 134
ABCABC = 134134 = 2*7*11*13*67
A+B+C = 1+3+4 = 8
Correctly solved by:
| 1. Dr. Hari Kishan |
D.N. College, Meerut, Uttar Pradesh, India |
| 2. Colin (Yowie) Bowey | Beechworth, Victoria, Australia |
| 3. Seth Cohen | Concord, New Hampshire, USA |
| 4. Kamal Lohia | Hisar, Haryana, India |
| 5. Riley Sack |
Central High School, Grand Junction, Colorado, USA |
| 6. Kelly Stubblefield | Mobile, Alabama, USA |