Latest MBA Aptitude Question SOLUTION: Remainder when (2222^5555 + 5555^2222) divided by 7 ?

1) 3
2) 2
3) 1
4) 0

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Remainder when (2222^5555 + 5555^2222) divided by 7 ?

1) 3
2) 2
3) 1
4) 0

Asked In MBA (11 years ago)

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Nithin Mnaikandan  (9 years ago)

Sol:

When 5555 and 2222 are divided by 7 we get the remainders 4 and 3 respectively.

so, problem reduces to find the remainder when 42222 + 35555 is divided by 7

so, 42222 + 35555 = (42)1111 + (35)1111

since, an + bn is divisible by (a + b) when n is ODD

therefore, it is divisible by 42 + 35 = 16 + 243 = 259

since, 259 is divisible by 7,

therefore, 7 will divide the 55552222 + 22225555

so, Remainder = 0

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Rahul Das  (8 years ago)

2222= 3 mod 7
5555 = 4 mod 7

2222^5555 + 5555^2222 = (3^5)^1111 + (4^2)^ 1111

as it is a^n + b^n and n is odd so it is divisible by

3^5 + 4^ 2 = 259

hence by 7 as 7 is a factor of 259

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