Data Sufficiency

Vincen wrote: ↑

Wed Jul 21, 2021 12:19 pm

A dental licensure exam requires a 75% minimum score in order to pass each section. Did Jennifer pass the 30-question third section?

(1) Jennifer recorded 8 more correct answers on the second half of the third section than she did on the first half of the third section.
(2) Jennifer answered one more question correctly on the third section than she did on the 28-question second section, which she passed.

Answer: A

Source: Veritas Prep

Given: A dental licensure exam requires a 75% minimum score in order to pass each section

Target question: Did Jennifer pass the 30-question third section?
75% of 30 = 22.5
So, in order to get at least 75% in the 3rd section, Jennifer must correctly answer 23 or more questions in the 3rd section.
REPHRASED target question: Did Jennifer correctly answer 23 or more questions in the 3rd section?

Statement 1: Jennifer recorded 8 more correct answers on the second half of the third section than she did on the first half of the third section.
Since there are 30 question in the third section, there are 15 questions in the 1st half and 15 questions in the 2nd half.
Let's examine ALL possible cases:
Case a: 0/15 correct in the 1st half and 8/15 correct in the 2nd half, for a total of 8/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case b: 1/15 correct in the 1st half and 9/15 correct in the 2nd half, for a total of 10/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case c: 2/15 correct in the 1st half and 10/15 correct in the 2nd half, for a total of 12/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case d: 3/15 correct in the 1st half and 11/15 correct in the 2nd half, for a total of 14/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case e: 4/15 correct in the 1st half and 12/15 correct in the 2nd half, for a total of 16/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case f: 5/15 correct in the 1st half and 13/15 correct in the 2nd half, for a total of 18/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case g: 6/15 correct in the 1st half and 14/15 correct in the 2nd half, for a total of 20/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case h: 7/15 correct in the 1st half and 15/15 correct in the 2nd half, for a total of 22/30. The answer to the REPHRASED target question is NO, Jennifer did NOT correctly answer 23 or more questions
Case i: 8/15 correct in the 1st half and 16/15 correct in the 2nd half. STOP. She can't get 16/15 correct. So, we've exhausted all possible cases.
Since our answer to the REPHRASED target question is the SAME every time, we can be certain that Jennifer did NOT correctly answer 23 or more questions
Statement 1 is SUFFICIENT

Statement 2: Jennifer answered one more question correctly on the third section than she did on the 28-question second section, which she passed.
We have no idea how many questions she answered correctly on the second section.
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent