The remainder of \(3^{560}/8\) is GMAT Problem Solving

Question: The remainder of \(3^{560}/8\) is:

A. 1
B. 7
C. 21
D. 27
E. 34

Answer: A

Approach Solution (1):
3⁵⁶⁰ = (3²)²⁸⁰ = 9²⁸⁰ 
9 leaves a remainder of 1 when divided by 8 and therefore 9²⁸⁰ leaves a remainder 1 (Remainder of product = Product of remainders)
Correct option: A

Approach Solution (2):
\(3^{560}/8\) = 3⁴ (140) /8 = 81¹⁴⁰/8
81¹⁴⁰/8 [r] = 1/8
Since 81/8 has remainder of 1
Sowill be
Remainder is 1
Correct option: A

Approach Solution (3):
3/8 leaves a remainder of 3
3²/8 = 9/8 leaves a remainder of 1
3³/8 = 27/8 leaves a remainder of 3
3⁴/8 = 81/8 leaves a remainder of 1
It looks like we have a 3-1 remainder pattern, which means the remainder will repeat twice (multiple of 2), therefore
Remainder of \(3^{560}/8\) = 1
Correct option: A

“The remainder of \(3^{560}/8\) is:”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question 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.

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