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Grade: 11
        Find sum of all the number greater than 10000 formed by the digits 0,2,4,6,8 no digit being repeted?
2 years ago

Answers : (1)

Arun
23032 Points
							
Dear Raj
 

1. Fix the units digit of the 5 digit number . say _ _ _ _ 2 
2. The total of such numbers with 2 in the units place is 4! i,e 24 
3. In the same manner there are 24 such numbers that end with 0,4,6 & 8 
4. Now the sum of all the numbers in the Units place is 
24 * (0+2+4+6+8) = 24 * 20 = 480 
5. The same is true for the 10th place, 100th place, 1000th place & 10,000th place. 
Hence the sum of all the 5 digit numbers using 0,2,4,6,8 is 
480 (1+10+100+1000+10000) 
= 480 (11111) 
5333280-----------------------------(A) 
6. Following the same approach as mentioned in steps 1 to 5, 
the sum of all the 4 digit numbers (5 digit numbers starting with 0 ) 
is 
= 6*(2+4+6+8)* (1+10+100+1000) 
= 6* 20 * 1111 
133320--------------------------------(B) 

7. Hence the sum of all the 5 digit numbers using 0,2,4,6,8 > 10000 
= (A) - (B) 
= 5333280 - 133320 

= 5199960 
 
Regards
Arun(askIITians forum expert)
2 years ago
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