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above720
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as Himalayan wisely wrote !

statement 1

2x + 2 is the cube of a positive integer.

f(2) = 2*2 + 2 = 6
cube(6) = not an integer

f(3) = 2*3 + 2 = 8
cube(8) = 2

f(5) = 2*5 + 2 = 12
cube(12) = not an integer

f(7) = 2*7 + 2 = 16
cube(16) = not an integer

f(31) = 2*31 + 2 = 64
cube(64) = 4

insufficient

statement 2

The average of any x consecutive integers is an integer

means only that x can't be 2 !

for (6,7) = (6+7)/2 = not an integer

insufficient

statement 1&2

still insufficient

so the answer is (E)



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