amitmj wrote:If there are more than 2 numbers in a certain list, is each of the numbers n the list equal to zero ?
1)The product of any 2 numbers in the list is ZERO
2)The sum of any 2 numbers in the list is ZERO
Target question: Is each of the numbers n the list equal to zero?
Given: There are more than 2 numbers in the list
Statement 1: The product of any 2 numbers in the list is ZERO
There are several possible sets that satisfy this condition. Here are two:
Case a: the set is {0, 0, 0} in which case
every number in the list is equal to ZERO
Case b: the set is {0, 0, 1} in which case
every number in the list is not equal to ZERO
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: The sum of any 2 numbers in the list is ZERO
This statement ensures that
every number in the list is equal to ZERO
Here's why:
Let's say the number k is in the set.
If any two numbers add to zero, then -k must be another number in the set.
At this point, we could have a set like {1, -1} where the numbers do not equal zero. Or we could have a set like {0, 0} where the numbers do equal zero. HOWEVER, we are told that the set has
more than 2 numbers.
So, what does a
third value look like?
Well, if we already have k in the set, then the third value must also be -k, otherwise we wouldn't get a sum of zero if we picked k and the third value.
At this point, we know that that the set must contain: k, -k, -k
[and possibly more values]
Now let's examine the pair of values -k and -k
If we add them, we get -2k. The ONLY way that this sum can equal zero if for k to equal zero.
We can extend this logic to conclude that
EVERY value in the set must equal ZERO
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
B
Cheers,
Brent
