Latest Elitmus Aptitude Question SOLUTION: Difference between sum of square of 2 digit odd number to sum of square of 2 digit even no.(11^2+13^2....-12^2+14^2....)

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Difference between sum of square of 2 digit odd number to sum of square of 2 digit even no.(11^2+13^2....-12^2+14^2....)

Asked In Elitmus AMBARISH SINGH (8 years ago)

Solved RAKESH Read Solution (6)

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RAKESH  (8 years ago) Best Solution

( 11^2 + 13^2 + .....+ 99^2 ) - ( 10^2 + 12^2 + .........+ 98^2 )

= (11^2 - 10^2) + (13^2 - 12^2) + ............+ (99^2 - 98^2).

= (11 + 10) + (13+12) +.........+(99+98)

= (10+11+12+13+......+98+99)

= (1+2+....+9+10+11+12+13+......+98+99) -(1+2+3+....+9)

= 99*100/2 - 9*10/2

= 4905

Is this solution Helpfull? Yes (53) | No (1)  

JUGAL KHAJURIYA  (8 years ago)

(11^2 + 13^2 + .....+ 99^2) - (10^2 + 12^2 + .........+ 98^2)
We can write this expr.
(11^2 - 10^2) + (13^2 - 12^2) + ............+ (99^2 - 98^2).
Again, we can split
(11 + 10)(11-10) +(13+12)(13-12) +.........(99+98)(99-98)
21 + 25 + 29 +.......197.
in a.p form
s=n(a+l)/2
s=45(21+197)/2
s=4905

Is this solution Helpfull? Yes (10) | No   

Abhishek Kumar  (8 years ago)

12^2-11^2=23
14^2-13^2=27
.
.
.
98^2-97^2=195
We get an AP as 23, 27, 31..........,195 with difference of 4
Adding this we get 4796
99^2-4796= 5005

Is this solution Helpfull? Yes (4) | No (6)  

Siddharth  (8 years ago)

(11^2 + 13^2 + .....+ 99^2) - (10^2 + 12^2 + .........+ 98^2)
we can write this expr.
(11^2 - 10^2) + (13^2 - 12^2) + ............+ (99^2 - 98^2).
again we can split
(11 + 10)(11-10) +(13+12)(13-12) +.........(99+98)(99-98)
21 + 25 + 29 +.......197.
in a.p form
ans== 4708

Is this solution Helpfull? Yes (2) | No (3)  

kaushal jaiswal  (8 years ago)

(12^2+14^2+......+98^2) - (11^2+13^2+......99^2)
12.2^(45-1) - (11.2^(44-1)) =2^43*23 ANS.

Is this solution Helpfull? Yes | No (9)  

Asmita  (8 years ago)

thnx @RAKESH :)

Is this solution Helpfull? Yes | No   

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