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
