What will be the remainder when 3^{136} is divided by 12 ?

- a)0
- b)3
- c)9
- d)None of the above

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

Related Test: CAT Quantitative Aptitude MCQ - 4

2 Answers

Vijish John
answered
Aug 20, 2020

I am unable to attach the picture of arriving at the answer. I will try to explain it in words.

On analysing we find that we get a remainder of 3 when dividing the 3 ^ odd numbers with 12 ie; 3^1 = 3/12, remainder is 3. 3^3 = 27/12, remainder is 3 etc. And, when dividing the 3 ^ even numbers with 12 ie; 3^2 = 9/12, remainder is 9. 3^4 = 81/12, remainder is 9 etc. Here, 136 is an even number. Hence, 3^136 will definitely give a remainder of 9. So, option c) is the answer.

On analysing we find that we get a remainder of 3 when dividing the 3 ^ odd numbers with 12 ie; 3^1 = 3/12, remainder is 3. 3^3 = 27/12, remainder is 3 etc. And, when dividing the 3 ^ even numbers with 12 ie; 3^2 = 9/12, remainder is 9. 3^4 = 81/12, remainder is 9 etc. Here, 136 is an even number. Hence, 3^136 will definitely give a remainder of 9. So, option c) is the answer.

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