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What is the remainder when 3^{6001} + 7^{6000} is divided by 13?

- a)9
- b)10
- c)4
- d)3

Correct answer is option 'C'. Can you explain this answer?

3^{6001} = 3 ⋅ (3^{6000}) = 3 ⋅ (3^{6})^{1000 }= 3 ⋅ (729)^{1000} = 3(728 + 1)^{1000}

728 is divisible by 13, so the remainder is 3.

7^{6000} = (7^{4})^{1500 }= (2401)^{1500 }= (2392 + 9)^{1500}2392 is divisible by 13, so we have to find the remainder when 9^{1500} is divided by 13.

9^{1500} = (3^{6})^{500} = (729)^{500} = (728 + 1)^{500}

since 728 is divisible by 13, therefore the remainder is 1.

So the net remainder = 3 + 1 = 4

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What is the remainder when 36001 + 76000 is divided by 13?a)9b)10c)4d)3Correct answer is option 'C'. Can you explain this answer? for CAT 2023 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What is the remainder when 36001 + 76000 is divided by 13?a)9b)10c)4d)3Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2023 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What is the remainder when 36001 + 76000 is divided by 13?a)9b)10c)4d)3Correct answer is option 'C'. Can you explain this answer?.

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36001 = 3 ⋅ (36000) = 3 ⋅ (36)1000 = 3 ⋅ (729)1000 = 3(728 + 1)1000728 is divisible by 13, so the remainder is 3.76000 = (74)1500 = (2401)1500 = (2392 + 9)15002392 is divisible by 13, so we have to find the remainder when 91500 is divided by 13.91500 = (36)500 = (729)500 = (728 + 1)500since 728 is divisible by 13, therefore the remainder is 1.So the net remainder = 3 + 1 = 4