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Given below two statements : Statement I : 25^13 + 20^13 + 8^13 + 3^13 is divisible by 7. Statement II : The integral part of (7 + 4√3)^25 is an odd number. In the light of the above statements, choose the correct answer from the options given below :

1. Both Statement I and Statement II are false.
2. Both Statement I and Statement II are true.
3. Statement I is false but Statement II is true.
4. Statement I is true but Statement II is false.

Correct answer: Both Statement I and Statement II are true.

Solution

Both statements are true; Statement I holds because the expression evaluates to a multiple of 7 when calculated modulo 7, and Statement II is true as the integral part of the expression results in an odd number.

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