CAT Exam 2015 preparation 5

A plot of land is divided into 50 parts: a₁, a₂, a₃, a₄, …, a₅₀.

M₁ = (a₁ + a₂ + a₃ + a₄ + … + a_i… + a₅₀)

 

M₂ = (a₁ a₂ + a₂ a₃ + a₁ a₃ + … + a_i a_j + … + a₄₉ a₅₀)

 

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M₅₀ = (a₁ a₂ a₃ …. a₅₀)

S = 1 + M₁ + M₂ + M₃ + … + M₅₀

Which of the following is true?

 

 

OPTIONS
	1)	S is odd if and only if all the ai’s are powers of two.
	2)	S is odd if and only if at least one of the ai’s is a power of two.
	3)	S is odd if and only if all the ai’s are odd.
	4)	S is odd if and only if all the ai’s are even.
	5)	None of these