Question: What is the Remainder When 3^243 is Divided by 5? GMAT Problem Solving
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“What is the remainder when 3^243 is divided by 5?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This GMAT Problem Solving topic has been taken from the book “GMAT Official Guide Quantitative Review.” To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
....
Unit digits for any power of three would be 1, 3, 7, or 9. We may have also noticed that the unit digit would repeat itself after every fourth power of 3.
As a result, the answer to the question would be 3^243 (or 3^(240+3)) with the unit digit 7
Therefore, when multiplied by 5, the remaining is 2.
Correct Answer: C
Approach Solution 2:
3^1/5 ..... Remainder = 3
3^2/5 ..... Remainder = 4
335 ..... Remainder = 2
3^4/5 ..... Remainder = 1
3^5/5 ..... Remainder = 3 & so on
So, the cyclicity of the remainder is 3,4,2,1.........
3^243/5 .... Remainder would be the same as 3^3/5 ..... Remainder = 2
Correct Answer: C
Approach Solution 3:
3^4= 1 (mod5)
3^243/5= (3^4)^60∗3^3/5= 1^60∗27/5
Remainder is 2.
Correct Answer: C
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