Passing the 30-question third section

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Passing the 30-question third section

by gmattesttaker2 » Mon Apr 28, 2014 11:11 pm
Hello,

Can you please assist with this:

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.


OA: A


Thanks a lot,
Sri

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by [email protected] » Mon Apr 28, 2014 11:28 pm
Hi Sri,

This DS question comes down to some specific math calculations.

We're told that to pass a dental exam, you need a minimum score of 75% (correct) in each section. The question asks if Jennifer passed the 30-question section. This is a YES/NO question.

The first required calculation is "what is 75% of 30?" That is 22.5, so the question is really asking "Did Jennifer answer at least 22.5 questions correctly?" This seems like an odd question to ask, since most tests don't give "half a point" when answering a question correctly. So this COULD mean "Did Jennifer answer at least 22.5 questions correctly?", but it's far more likely to mean "Did Jennifer answer at least 23 questions correctly?"

Fact 1: Jennifer recorded 8 more correct answers on the SECOND HALF of the section than she did on the FIRST HALF of the section.

With 30 questions in this section, the first half = 15 questions and the second half = 15 questions. Let's TEST VALUES....I'm going to focus on the minimum and maximum possible results....

If she got correct....
0 in the first half and 8 in the second half, then she scored 8/30 and the answer to the question is NO. (this is the minimum result)
7 in the first half and 15 in the second half, then she scored 22/30 and the answer to the question is NO. (this is the maximum result)
Under these conditions, the answer is ALWAYS NO.
Fact 1 is SUFFICIENT

Fact 2: Jennifer answered 1 MORE question correctly than she did on the 28 question second section, which she passed.

Here, 75% of 28 = 21, so we know she answered AT LEAST 21 questions correctly in the second section and AT LEAST 22 questions correctly in the third section.

If she answered 22 correctly, then she scored 22/30 and the answer to the question is NO.
If she answered 23 correctly, then she scored 23/30 and the answer to the question is YES.
Fact 2 is INCONSISTENT

Final Answer: A

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by Brent@GMATPrepNow » Fri Jan 18, 2019 7:29 am
gmattesttaker2 wrote:Hello,

Can you please assist with this:

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.


OA: A


Thanks a lot,
Sri
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 b: 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
Brent Hanneson - Creator of GMATPrepNow.com
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