Data Sufficiency

BTGmoderatorDC wrote: ↑

Mon Jan 09, 2023 6:48 pm

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.


OA B

Source: GMAT Prep

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