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05 Aug 2026, 22:56
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At a science quiz, Team Atlas consisted of Elena, Hugo, and Liam, and Team Nova consisted of Mia, Theo, and Nora. If a team’s score was the average (arithmetic mean) of the three scores earned by its members, what was Team Atlas’s score?
(1) Elena scored 15 points more than Mia, Hugo scored 6 points fewer than Theo, and Liam scored 18 points fewer than Nora.
(2) If Mia had scored 18 points more, Team Nova’s score would have been 20% greater than Team Atlas’s score.
(1) Elena scored 15 points more than Mia, Hugo scored 6 points fewer than Theo, and Liam scored 18 points fewer than Nora.
(2) If Mia had scored 18 points more, Team Nova’s score would have been 20% greater than Team Atlas’s score.
05 Aug 2026, 22:56
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Official Solution:
At a science quiz, Team Atlas consisted of Elena, Hugo, and Liam, and Team Nova consisted of Mia, Theo, and Nora. If a team’s score was the average (arithmetic mean) of the three scores earned by its members, what was Team Atlas’s score?
Let \(A\) be Team Atlas’s score, and let \(N\) be Team Nova’s score. The question asks for \(A\).
(1) Compare the total scores of the two teams.
• Elena scored 15 more than Mia.
• Hugo scored 6 fewer than Theo.
• Liam scored 18 fewer than Nora.
So Team Atlas’s total score was:
\(15 - 6 - 18 = -9\)
Thus, Team Atlas’s total score was 9 points less than Team Nova’s total score.
Since each team has 3 members, the difference between the team averages is:
\(\frac{9}{3} = 3\)
Therefore:
\(A = N - 3\)
This gives only the relationship between the two team scores, not the actual value of \(A\).
Not sufficient.
(2) If Mia had scored 18 points more, Team Nova’s total score would have increased by 18 points.
Since Team Nova has 3 members, its average score would have increased by:
\(\frac{18}{3} = 6\)
So the adjusted Team Nova score would have been:
\(N + 6\)
Statement (2) says this adjusted score would have been \(20\%\) greater than Team Atlas’s score:
\(N + 6 = 1.2A\)
This gives only a relationship between \(A\) and \(N\), not the actual value of \(A\).
Not sufficient.
(1)+(2)
From statement (1): \(A = N - 3\)
From statement (2): \(N + 6 = 1.2A\)
Solving gives \(A = 45\). So Team Atlas’s score is determined.
Sufficient.
Answer: C
At a science quiz, Team Atlas consisted of Elena, Hugo, and Liam, and Team Nova consisted of Mia, Theo, and Nora. If a team’s score was the average (arithmetic mean) of the three scores earned by its members, what was Team Atlas’s score?
Let \(A\) be Team Atlas’s score, and let \(N\) be Team Nova’s score. The question asks for \(A\).
(1) Compare the total scores of the two teams.
• Elena scored 15 more than Mia.
• Hugo scored 6 fewer than Theo.
• Liam scored 18 fewer than Nora.
So Team Atlas’s total score was:
\(15 - 6 - 18 = -9\)
Thus, Team Atlas’s total score was 9 points less than Team Nova’s total score.
Since each team has 3 members, the difference between the team averages is:
\(\frac{9}{3} = 3\)
Therefore:
\(A = N - 3\)
This gives only the relationship between the two team scores, not the actual value of \(A\).
Not sufficient.
(2) If Mia had scored 18 points more, Team Nova’s total score would have increased by 18 points.
Since Team Nova has 3 members, its average score would have increased by:
\(\frac{18}{3} = 6\)
So the adjusted Team Nova score would have been:
\(N + 6\)
Statement (2) says this adjusted score would have been \(20\%\) greater than Team Atlas’s score:
\(N + 6 = 1.2A\)
This gives only a relationship between \(A\) and \(N\), not the actual value of \(A\).
Not sufficient.
(1)+(2)
From statement (1): \(A = N - 3\)
From statement (2): \(N + 6 = 1.2A\)
Solving gives \(A = 45\). So Team Atlas’s score is determined.
Sufficient.
Answer: C
