During a penalty-scored trivia challenge, Sophia worked through a set

Question

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.

Bunuel · Accepted Answer

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.

AdarshSambare · Answer

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

SS990 · Answer

The answer is C
WE know, correct is 5, incorrect is -3 and UA is -2. To det is no of questions n<7

1) Score=18 
We can get 18 with n=5 if 5*4=20 and 1 UA with -2, totalling to 18

WE can also get by having Correct=5*5=25 and to get 18 we need a -7 which is 1 inccorect and 2 UA questions. Totally 8 questions.
SO this is insuffciient

2) atleast 1C, 1 IC and 1 UA. But this can be achieved with lets say 2C, 1IC and 1A or seeral other ombinations. This is given to confuse you with the prev 18marks condition in to think this should suffice. In any case, this choice gives innumerable no of choices.

Together, we know score has to be 18 and atleast 1C, 1 IC and 1 UA. If at all there is a choice less than 7 tht can accomodate the conditions it may be 6 because from 5 and below the above condition is straight away lower than 18 score. and with 6 this combo is not possible. Hence no. of questions has to be greater than 7. so C is the answer

Adit_ · Answer

When you took the cases for together,
First one would lead to a value <18.

pappal · Answer

its for sure that individual 1 and 2 are non sufficient. 
taking together;
condition 2 states that at least one belongs to each category summing up to 3 questions but adding ZERO to the score.
now from 1, to get a score of 18 there may be different choices but its for sure that minimum no. of correct questions should be greater than or equal to 4.
eg 5*4 - 2*1 or 5*5 - 1*3 -2*2 etc
hence for certain total questions are not less than 7.
C

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