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| Answer:Answer: 1080. |
| Generic method: |
| If we consider two digit positive numbers formed by even digits, they start with 20, 22, 24, 26 and 28; |
| then 40, 42, 44, 46 and 48; similarly in 60s and 80s. |
| If we write 20 + 22 + 24 + 26 + 28 as 20 x 5 + (2 + 4 + 6 + 8), we get the sum as 120. |
| Similarly 40 + 42 + 44 + 46 + 48 = 40 x 5 + (2 + 4 + 6 + 8) = 220. |
| Using this pattern, |
| the total sum of two digit numbers that contain only even digits = 120 + 220 + 320 + 420 = 1080. |
| Statistics method: |
| For framing a two digit number that contain only even digits, we need to fill two places |
| namely units place and tens place. |
| Units place can be filled in 5 ways with any of the five digits 0, 2, 4, 6, 8. |
| Tens place can be filled in 4 ways with any of the four digits 2, 4, 6, 8. |
| If we place 0 in tens place, then it becomes a single digit number. |
| The sum of all the two digit numbers formed by even digits is nothing but |
| the sum of all tens place digits multiplied by 10 + sum of all the units place digits. |
| So the sum of all the two digit numbers formed by even digits = (2 + 4 + 6 + 8) x 5 x 10 + (0 + 2 + 4 + 6 + 8) x 4 = 1080. |
| Winners:Rajeswararao Ainapurapu, Sumanth Nethi, Sarvani Kunapareddy, Raghu Ayinapurapu. |
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