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.


2) in order for the sum of "any 2 numbers" to = 0, all the numbers must equal 0
SUFFICIENT

1) in order for the product of "any 2 numbers" to = 0, wouldn't all the numbers in the set also have to = 0?

however, the answer is B. where am I going wrong? thanks

For 1) try this scenario, all numbers except one number are zero's. In this case the product of any two numbers is 0. Hence INSUFFICIENT.

-Raj.

thanks raj

I have a doubt. In this question, it isnnot given that list contains positive numbers. So we can consider negative numbers also. In that case, it is not necessary that the sum of any two numbers in the list is equal to 0 if all the numbers are zero.
Eg: we can consider -2, 2
their sum is zero.
Please clarfify

Taking GMAT,

yes -2 + 2 = 0, however, statement 2 gives: the sum of ANY TWO...
So, since there are "more than 2" numbers in the set, the set contains (in your example): (-2, 2, x). because the set contains at least that x, the sum of "any 2" numbers, for instance 2 + x, does not have to equal zero.
so, INSUFFICIENT

i know that i just answered this question last week. i hate the google box.

this objection won't work, because you need to have more than 2 numbers in the set. the problem is that ANY two numbers have to sum to zero - which means that if you pair the mystery third number with EITHER of the existing two numbers, you must get a sum of zero.

if your first two numbers are 2 and -2, that's impossible: there's no number that will add to 2 to give zero, and will ALSO add to -2 to give zero.

in general, if your first two numbers are -x and x, then your third number must be x (so that it adds to -x to give zero), but it must ALSO be -x (so that it adds to x to give zero). the only way that x can equal -x is if x is zero - which means that all three numbers are zero.

therefore, everything must be zero.

As a non-native English speaker, when I read ANY TWO, I still assume that a list with exactly TWO elements is acceptable. So is this down to English, or am I assuming wrong?

the problem statement says that the list contains more than two entries.

Thanks... my common mistake.. reading to fast and not paying attention to details..

it's a very common story.
in fact, when people have trouble on data sufficiency problems, very rarely does that trouble have its roots in the actual mathematics. instead, the trouble usually comes from the data sufficiency format itself, or other underlying points of strategy/technique that are very close to the ground.

if you are making these kinds of mistakes on data sufficiency but not also on problem solving, then the confusion most likely stems from the weirdness of the data sufficiency format. i.e., the problems are strange, so your mind gets more occupied when you solve them, so you have less attention to pay to stuff like this.

the key is to remember that you -- individually -- have a track record of not noticing conditions stated in the problem. therefore, you should always double-check all stated conditions.
if you consistently switch positive/negative signs, then you should double-check all signs (even if other people may not have to).
that's the secret, which isn't really a secret.