If there are more than two numbers is a certain list, is

Question

If there are more than two numbers is a certain list, is each number in the list equal to 0?
1) Product of any two numbers in the list is equal to 0.
2)The sum of any two numbers in the list is equal to 0.

old_dream_1976 · Answer

there are more than 2 numbers - and sum of all is equal to zero

ywilfred · Answer

St1:
Insufficient.

As long as the list has all 0, and any one number is non-zero, the product of any two numbers from this list will always be 0. 

Similarly, if all numbers in this list is 0, then the product of any two numbers is also 0.

St2:
Sufficient.

We now the list must be all 0.

Ans B

BG · Answer

Hallo,
Agree with old dream, numbers are more than 2 so B)
Regards

remgeo · Answer

It doesnt say, sum of ALL nos is 0. 
It says sum of any 2 nos is 0. In that case, your situation does not hold. 

So it has to be B.

Professor · Answer

has to be B. 

from i, if list consists numbers 0, 0, and 1, product of any two numbers is 0. 
from ii, list must contain more than 2 numbers. therefore, the numbers must be all 0s. 
so suff and B is it.

shevy · Answer

Agree with B :wink:

Dilshod · Answer

It is B, because:
St.1 insuff: consider 0,0,1 or 0,0,0.
St 2 suff: since there are more than 2numbers, the sum of any 2 numbers in the set can equal to 0 only if each member of the set is 0.

necromonger · Answer

B

(If it was just 2 numbers then it would be C.. but if there are more than 2 numbers, then there's no way to get 0 for any two additions unless all are 0)

HongHu · Answer

Good point. To prove it, try three numbers. a+b=0, b+c=0, a+c=0. Add them up you get 2(a+b+c)=0 and thus a+b+c=0.

If there are more than two numbers is a certain list, is

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