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SSC Selection Post 2019 PYQ — Question 66

SSC Selection Post - Matriculation Level 2019 - 15 Oct 2019 • Quantitative Aptitude • Q66

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When (236-1) is divided by 9, the remainder is:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 0.

236−1=(218+1)(218−1)218−1=(26)3−13=a3−b3=(a−b)(a2+ab+b2)2^{36} - 1 = (2^{18} + 1)(2^{18} - 1) 2^{18} - 1 = (2^6)^3 - 1^3 = a^3 - b^3 = (a - b)(a^2 + ab + b^2)

=(64−1)(642+64×1+1)= (64 - 1)(64^2 + 64 \times 1 + 1)  = 63 × some integer 

Since 63 ÷ 9 = 7 , divisible by 9

so remainder = 0