Latest CAT Aptitude Question SOLUTION: If x=(16^3+17^3+18^3+19^3),then x divided by 70 leaves a remainder of 1>0 2>1 3>69 4>35

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(#M40013464) CAT question CAT Keep an EYE

If x=(16^3+17^3+18^3+19^3),then x divided by 70 leaves a remainder of
1>0
2>1
3>69
4>35

Asked In CAT Awadhesh Kumar (11 years ago)

Solved Kalidas Read Solution (3)

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Kalidas  (11 years ago)

x=(16^3+17^3+18^3+19^3)= 21700
21700/70 = 310


If x=(16^3+17^3+18^3+19^3),then x divided by 70 leaves a remainder of '0' (ZERO)

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Dushyant Kumar  (11 years ago)

16^3+19^3+17^3+18^3=(16+19)^3-3*16*19(16+19)+(17+18)^3-3*17*18(17+18)
=(35)^3-70*(3*8*19)+(35)^3-70*(3*17*9)
=(35+35)^3-3*35*35(70)-70*((3*8*19)+(3*17*9))
=(70)^3-70*(3*35*35)-70*((3*8*19)+(3*17*9))
since all factors are in multiple of 70
answer is ZERO (0)

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Amit kumar  (11 years ago)

x= p+q
let p= 16^3+18^3 (Even+Even=Even) and q= 17^3++19^3(Odd+Odd=Even)
===>{{concept P^n+Q^n is divisible by P+Q when n is odd}}
p is divisible by 2 and 35 it means p divided by 70.
q is also divisible by 2 and 35 it means q divided by 70.
So X is also decided by 70. Th remainder is 0.

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