Find sum of all the number greater than 10000 formed by the digits 0,2,4,6,8 no digit being repeted?
Raj kumar , 7 Years ago
Grade 11
Magical Mathematics[Interesting Approach]> Find sum of all the number greater than 1...
1 AnswersArun
Last Activity: 7 Years ago
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
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)
Provide a better Answer & Earn Cool Goodies
Enter text here...
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Ask a Doubt
Get your questions answered by the expert for free
Enter text here...
Other Related Questions on magical mathematics[interesting approach]
Given that (1+5x)⁴ = 1 + Px + Qx² + Rx³ +..... Find the values of P - 2Q + 3R
magical mathematics[interesting approach]
1 Answer Available
Last Activity: 2 Years ago
9 men and 15 boys working 10 hours a day can make 12 pillars in 42 days, in how many days will 12 men and 22 boys working 8 hours a day can make pillars 4 times the previous number?
magical mathematics[interesting approach]
1 Answer Available
Last Activity: 2 Years ago
In the given figure, PQ is a tangent at a point C to a circle with centre O. If AB is a diameter, find angle PCA + angle BCQ?
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 2 Years ago
for any two sets A and B (A-B)U(B-A)U (A intersection B)
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 2 Years ago
If someone has got 150 out of 200 marks in term 1 exam and 160 out of 200 marks in term 2 exam then what is the percentage in30:70
magical mathematics[interesting approach]
0 Answer Available
Last Activity: 3 Years ago