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Ipshit Tarun

· started a discussion

· 1 Months ago

What is the logic (Question: 355987.0 )

Ye kya kuch bhi kar dia.. Please explain

Question:

Find the remainder when 22225555 + 55552222 is divided by 7.

Options:
A)

1

B)

0

C)

2

D)

5

Solution:

Ans: (b)

  


The remainders when 5555 and 2222 are divided by 7 are 4 and 3 respectively.


Hence, the problem reduces to finding the remainder when


4^2222 + 3^ 5555 is divided by 7.

3^5555 +4^2222 

=3^5*1111 +4^2*1111

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

=243^1111 +16^1111

Which is divisible by 243+16=259

[x^n + y^n always divisible by x+y if n is odd]

But 259 is divisible by 7

Therefore 3^5555 + 4^2222 is divisible by 7

Therefore remainder is zero.

Knowledge Expert

· commented

· 1 Months ago

Dear Student,
Refer this solution ,

The remainders when 5555 and 2222 are divided by 7 are 4 and 3 respectively.

Hence, the problem reduces to finding the remainder when

4^2222 + 3^ 5555 is divided by 7.
3^5555 +4^2222
=3^5*1111 +4^2*1111
=(3^5)^1111 +(4^2)^1111
=243^1111 +16^1111
Which is divisible by 243+16=259
[x^n + y^n always divisible by x+y if n is odd]
But 259 is divisible by 7
Therefore 3^5555 + 4^2222 is divisible by 7
Therefore remainder is zero.

Thanks and Regards
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