GMAT Club World Cup 2022 (DAY 2): List A consists of n integers. One

Statement (1) alone:
If A is {0,1,2} and B is {0,1}, the average of A is not equal to the average of B.
If A is {0,1,2} and B is {0,2}, the average of A is equal to the average of B.
Do we have enough information from statement (1) alone to know whether the average of A is equal to the average of B? No. BCE.

Statement (2) alone:
If A is {-3,0,1,2} and B is {0,1,2}, the average of A is not equal to the average of B.
If A is {-3,0,1,2} and B is {-3,1,2}, the average of A is equal to the average of B.
Do we have enough information from statement (2) alone to know whether the average of A is equal to the average of B? No. CE.

Statements (1) and (2) together:
We know from the words "exactly half" that we must have an even number of elements in A. And since the sum of A is odd, we know that we have an odd number of odd elements (which means that we also have an odd number of even elements, which means that we have an even total number of elements). The average of A is therefore an odd divided by an even. The average of B will either be an odd divided by an odd or an even divided by an odd. Either way, it's not going to equal the average of A.
Do statements (1) and (2) together give us enough information to know whether the average of A is equal to the average of B? Yes. C.

Answer choice C.

List A consists of n integers. One number is removed from list A, and the remaining numbers comprise list B. Is the average (arithmetic mean) of the numbers in list A equal to the average (arithmetic mean) of the numbers in list B?


(1) The sum of the numbers in list A is an odd number

Let the numbers be 5, 5, 7, 8, and 10. Their sum is an odd number 35 and average is 7. If I take out 7 from the set and calculate the average, it’s still 7. Yes answer. However, if I take any other number, the average will change. So, No answer.
Insufficient.



(2) Exactly half of the numbers in list A is positive

This statement informs that the number of integers set A has is EVEN. So, let the numbers be -3, 0, 1, and 2 whose average is 0. If I exclude 0 from the set, the mean is still 0. We have Yes answer. If I take out any other number, the answer is No.
Insufficient.



1+2) So we know that the average for set A looks as ODD/EVEN which ends anyway with decimal …,5 (for example; 2,5 or 3,5 or 100,5 that ends anyway with 5)

If we exclude any number from set A, we will have either ODD/ODD or EVEN/ODD whose decimal representation never ends with 5. So, averages are not equal.


So C