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10 May 2026, 19:00
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C
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Difficulty:
(N/A)
Question Stats:
36% (02:19) correct
64%
(02:03)
wrong
based on 11
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During a trivia contest, Sophia completed a set of trivia questions. Each question in the set could have been answered correctly, answered incorrectly, or left unanswered. If a correct answer was worth 5 points, an incorrect answer reduced the score by 3 points, and an unanswered question reduced the score by 2 points, did the set contain fewer than 7 questions?
(1) Sophia’s final score was 18 points.
(2) Sophia answered at least one question correctly, answered at least one question incorrectly, and left at least one question unanswered.
(1) Sophia’s final score was 18 points.
(2) Sophia answered at least one question correctly, answered at least one question incorrectly, and left at least one question unanswered.
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11 May 2026, 01:30
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GMAT Club Official Solution:
During a trivia contest, Sophia completed a set of trivia questions. Each question in the set could have been answered correctly, answered incorrectly, or left unanswered. If a correct answer was worth 5 points, an incorrect answer reduced the score by 3 points, and an unanswered question reduced the score by 2 points, did the set contain fewer than 7 questions?
Let C be the number of questions Sophia answered correctly, I be the number she answered incorrectly, and U be the number she left unanswered.
The question asks whether C + I + U < 7.
(1) Sophia’s final score was 18 points.
This give:
5C - 3I - 2U = 18
If C = 4, I = 0, and U = 1, then the score is 20 - 2 = 18, and the total number of questions is 5, which is fewer than 7.
If C = 5, I = 1, and U = 2, then the score is 25 - 3 - 4 = 18, and the total number of questions is 8, which is not fewer than 7.
Not sufficient.
(2) Sophia answered at least one question correctly, answered at least one question incorrectly, and left at least one question unanswered.
This tells us only that C, I, and U are all positive.
Not sufficient.
(1)+(2) From (1):
5C - 3I - 2U = 18
So:
5C = 18 + 3I + 2U
From statement (2), I >= 1 and U >= 1. Therefore:
5C >= 18 + 3 + 2
5C >= 23
Since C is an integer, C >= 5. Also, from statement (2), I >= 1 and U >= 1. Thus:
C + I + U >= 5 + 1 + 1 = 7
So the set cannot contain fewer than 7 questions. The answer to the question is no.
Sufficient.
Answer: C.
During a trivia contest, Sophia completed a set of trivia questions. Each question in the set could have been answered correctly, answered incorrectly, or left unanswered. If a correct answer was worth 5 points, an incorrect answer reduced the score by 3 points, and an unanswered question reduced the score by 2 points, did the set contain fewer than 7 questions?
Let C be the number of questions Sophia answered correctly, I be the number she answered incorrectly, and U be the number she left unanswered.
The question asks whether C + I + U < 7.
(1) Sophia’s final score was 18 points.
This give:
5C - 3I - 2U = 18
If C = 4, I = 0, and U = 1, then the score is 20 - 2 = 18, and the total number of questions is 5, which is fewer than 7.
If C = 5, I = 1, and U = 2, then the score is 25 - 3 - 4 = 18, and the total number of questions is 8, which is not fewer than 7.
Not sufficient.
(2) Sophia answered at least one question correctly, answered at least one question incorrectly, and left at least one question unanswered.
This tells us only that C, I, and U are all positive.
Not sufficient.
(1)+(2) From (1):
5C - 3I - 2U = 18
So:
5C = 18 + 3I + 2U
From statement (2), I >= 1 and U >= 1. Therefore:
5C >= 18 + 3 + 2
5C >= 23
Since C is an integer, C >= 5. Also, from statement (2), I >= 1 and U >= 1. Thus:
C + I + U >= 5 + 1 + 1 = 7
So the set cannot contain fewer than 7 questions. The answer to the question is no.
Sufficient.
Answer: C.
General Discussion
10 May 2026, 20:51
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From (1):
5c − 3i − 2u = 18
Possible totals:
c=4, i=0, u=1 → total = 5
c=6, i=4, u=0 → total = 10
Not sufficient.
From (2):
We only know at least one correct, one incorrect, and one unanswered question.
Not sufficient.
Together:
c=4, i=1, u=1 → total = 6
c=5, i=1, u=2 → total = 8
Different answers are possible, so cannot determine.
Answer: E
5c − 3i − 2u = 18
Possible totals:
c=4, i=0, u=1 → total = 5
c=6, i=4, u=0 → total = 10
Not sufficient.
From (2):
We only know at least one correct, one incorrect, and one unanswered question.
Not sufficient.
Together:
c=4, i=1, u=1 → total = 6
c=5, i=1, u=2 → total = 8
Different answers are possible, so cannot determine.
Answer: E
