An instructor scored a student's test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?
A. 19
B. 38
C. 41
D. 44
E. 46
The OA is E.
Here's an approach to solving this question,
x  #of correct answers
y  # of incorrect answers
x + y = 50
x  2y = 38
So 3y = 12 => y = 4, so x = 46.
Has anyone another strategic approach to solve this PS question? Regards!
An instructor scored a student's test of 50 questions by
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Hi All,
We're told that an instructor scored a student's test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers and that the student answered all of the questions and received a score of 38. We're asked for the number of questions the student answered correctly. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.
To start, it's important to recognize that while each correct answer gains us 1 point, each incorrect answer 'costs' us 2 POINTS. Thus, to score 38 on the Exam, you need far MORE than 38 correct answers. Thus, let's start with one of the bigger answers...
Answer D: 44
With 44 correct answers and 6 incorrect answers, the score result would be...
44  2(6) = 44  12 = 32
This is TOO LOW (the score is supposed to be 38), so we clearly need MORE correct answers.
There's only one answer that fits...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
We're told that an instructor scored a student's test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers and that the student answered all of the questions and received a score of 38. We're asked for the number of questions the student answered correctly. This question can be solved in a couple of different ways, including by TESTing THE ANSWERS.
To start, it's important to recognize that while each correct answer gains us 1 point, each incorrect answer 'costs' us 2 POINTS. Thus, to score 38 on the Exam, you need far MORE than 38 correct answers. Thus, let's start with one of the bigger answers...
Answer D: 44
With 44 correct answers and 6 incorrect answers, the score result would be...
44  2(6) = 44  12 = 32
This is TOO LOW (the score is supposed to be 38), so we clearly need MORE correct answers.
There's only one answer that fits...
Final Answer: E
GMAT assassins aren't born, they're made,
Rich
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Letting C = the number of correct answers and W = the number of incorrect answers, we can create the equations:AAPL wrote:An instructor scored a student's test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?
A. 19
B. 38
C. 41
D. 44
E. 46
C + W = 50
W = 50  C
and
C  2W = 38
Substituting, we have:
C  2(50  C) = 38
C  100 + 2C = 38
3C = 138
C = 46
Alternate Solution:
Let's test each answer choice. Notice that the number of questions answered correctly cannot be less than or equal to the final score, thus we can immediately eliminate answer choices A and B (the number of correct answers is equal to the final score only if a student answer all questions correctly).
Answer Choice C: 41 correct answers, 9 false answers
Since 41  2*9 = 23, C is not the correct choice.
Answer Choice D: 44 correct answers, 6 false answers
Since 44  2*6 = 32, D is not the correct choice.
At this point, we know the answer must be E since we eliminated every other possibility, but let's verify it anyway.
Answer Choice E: 46 correct answers, 4 false answers
Since 46  2*4 = 38, E is the correct choice.
Answer: E
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STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?AAPL wrote: ↑Tue Jul 03, 2018 5:31 amAn instructor scored a student's test of 50 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions and received a score of 38, how many questions did that student answer correctly?
A. 19
B. 38
C. 41
D. 44
E. 46
In this case, we can easily test the answer choices.
At this point, we should typically give ourselves 15 to 20 seconds to identify a faster approach, but testing the answer choices will be incredibly easy, and I'm pretty sure I'll need to test 2 answer choices at most. So, I'll start testing the answer choices immediately.
We'll start with answer choice C  41
There are 50 questions and total.
If the student correctly answered 41 questions, we know that the student incorrectly answered 9 questions.
Total score =41  (2)(9) = 41  18 = 23
Since we're told the students received a score of 38, we know that answer choice C is incorrect.
It's also clear that, in order to achieve a score of 38, the student must get more than 41 questions right, which means we can also eliminate answer choices A and B.
MORE STRATEGY: At this point, I need only test ONE answer choice. For example, if I test answer choice D and it works, then I know the correct answer is D. Alternatively, if I test answer choice D and it doesn't work, then I know the correct answer is E.
Let's test choice D  44
So, if the student correctly answered 44 questions, we know that the student incorrectly answered 6 questions.
Total score =44  (2)(6) = 44  12 = 32
Since we're told the students received a score of 38, we know that answer choice D is incorrect.
By the process of elimination, the correct answer must be E.

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If we let X equal the number of answers that are correct and W equal the number of answers that are incorrect, then we can create the following equations:
X + W = 50
W = 50  X
and X  2W = 38
When we make this exchange, we get:
X  2(50  X) = 38
X  100 + 2X = 38
3X = 138
X = 46
X + W = 50
W = 50  X
and X  2W = 38
When we make this exchange, we get:
X  2(50  X) = 38
X  100 + 2X = 38
3X = 138
X = 46