Data Sufficiency

If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0?
1) The 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.
IMO C [spoiler]OA: B[/spoiler]

the correct answer is B

to check we need to familiarize ourselves with signs/0 number properties and other arithmetic concepts

the product of two or more numbers will be 0 if any of the numbers is 0 (not necessarily all the numbers must be 0), hence st(1) is Not Sufficient => with three numbers two are 0 one is not 0; more than three numbers all must be 0.

in statement (2) we consider sum which is equal to 0. This is possible only if the numbers are 0 or the numbers are having opposite signs with the same modes. We realize the latter is not possible for more than two numbers, therefore our answer is Yes and all numbers are 0, select B.

vishal.pathak wrote:If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0?
1) The 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.
IMO C [spoiler]OA: B[/spoiler]

Thanks Pemdas, Nice explanation! Here is how I see it

If there are more than two numbers in a certain list, is each of the numbers in the list equal to 0?

1) The product of any two numbers in the list is equal to 0.

Let us assume that the total number of numbers in the list be 3(The below solution is valid for any number of total numbers)

Case 1: Let the list be s = {0,0,0}
0*0=0*0=0*0=0. Satisfies the condition 'The product of any two numbers in the list is equal to 0'and we can say that each of the numbers in the list is equal to 0

Case 2: Let the list be s = {0,0,2}
0*0=2*0=0*2=0. Satisfies the condition 'The product of any two numbers in the list is equal to 0' and we can say that each of the numbers in the list need not be equal to 0. Hence Insufficient.

2) The sum of any two numbers in the list is equal to 0.

Let us assume that the total number of numbers in the list be 3(The below solution is valid for any number of total numbers)
Let the list be s = {a,b,c}
From the condition B)
a + b = 0 - (1)
b + c = 0 - (2)
c + a = 0 - (3)
Adding the equations (1),(2),(3) above we get a + b + c = 0 - (4)
Equation (4)-(1) a + b + c - (a + b) = 0 => c = 0
From equation (2) b + c = 0 => b + 0 = 0 => b = 0
From equation (1) a + b = 0 => a + 0 = 0 => a = 0
So, a=b=c=0.
Hence Sufficient to answer the question!

Option B