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The sequence S consists of 10 terms: x, x^2, x3, ..., x^10, where x is a non-zero number. Is the sum of all the terms in the sequence greater than 0?

(1) The distance of any term of the sequence S from zero on the number line is not less than 1.

|x |>= 1 ..

if x=1 ... sum >0 .. If x=-1 , sum =0 . So not sufficient .

(2) x^5 = x^7


X can be 1 or -1 .
So we have 2 case as discussed above . So not sufficient .

Combining 1 and 2 also , we have the same case . So not sufficient .

Hence E .
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The distance of any term of the sequence S...why do we need to consider x. Please explain. I did like this. Check if
( sum of odd powered terms - sum of even powered terms) < 0.
sum of odd powered terms < 0
Hence, each term must be less than 0.
Statement 1 says no term less than 1 so sufficient.

Please explain where I did wrong.

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PRAJESH0133

The word "distance" means x can be +1 away from 0 or -1 away from 0. Thus we can have x = 1.5 for example and the terms keep on getting bigger, or x = -1 and we would have 5 negative terms 5 positive terms which add up to 0.
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The sequence S consists of 10 terms: x, x^2, x3, ..., x^10, where x is a non-zero number. Is the sum of all the terms in the sequence greater than 0?

(1) The distance of any term of the sequence S from zero on the number line is not less than 1.
(2) x^5 = x^7

(1). Not Sufficient,
as per this statement, X is not less than one. so sum of x,x^2.....can not be found and if X=0, sum= 0,
X>=1, Sum>0, X=-1, Sum=0 etc. so not sufficient.

(2) Not Sufficient.
X^5=X^7, only possible for X=0, 1 & -1.
X=1 gives Sum>0, X=0 & -1 gives Sum=0,

Both statement together also doesn't provide any additional info. so both statements together are also not sufficient.
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Bunuel
The sequence S consists of 10 terms: x, x^2, x3, ..., x^10, where x is a non-zero number. Is the sum of all the terms in the sequence greater than 0?

(1) The distance of any term of the sequence S from zero on the number line is not less than 1.
This can lead to a large no of possibilities ranging from a difference that can 2 , 4 ,6 and even negative
Clearly insufficient

(2) x^5 = x^7
This possibilities can only arise if x=1 and when x=-1

even when 1 and 2 is combined we get
x can be equal to 1 or -1 which will lead to different possibilities

Therefore IMO E
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