Choose given statement is true or false:

In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, and -40 in three successive rounds. Both the teams get equal points at the end of the quiz even if the scores are added in different order. So, can we say that we can add integers in any order ?

Question

Choose given statement is true or false:

In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, and -40 in three successive rounds. Both the teams get equal points at the end of the quiz even if the scores are added in different order. So, can we say that we can add integers in any order ?

Accepted Answer

The given statement is true.
Concept: The team's total score is the sum of the scores for each round. Simply add up the results of individual rounds to get the final score for each team.
Team A will now score -40, 10, and 0 in Rounds 1, 2, and 3, respectively.
Therefore, the total score of Team A at the end of the quiz is

Currently, Team B scores in Rounds 1, 2, and 3 are 10, 0, and -40, respectively.
Therefore, the total score of Team B at the end of the quiz is

From equations (1) and (2), it can be clearly stated that the total score of Team A and Team B after the quiz is -30. Therefore, no team scored any more points and both were tied at the end of the quiz. Yes, you can add integers in any order.
Seen from above, the different round results for Teams A and B meant adding the same numbers, -40, 0, 10 in a different order, but the additions are still the same, even if the order is different. Therefore, the statement is absolutely true.
Hence, the given statement is true.