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# An instructor scored a students test of 50 questions by subtracting 2

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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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If x is the number of mistakes, then the score is (50-x)-2x=50-3x
50-3x=38
3x=12
x=4

So, the number of right answers is 50-4=46. The answer is E
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Yeah common sense tells me answer will be greater than 38. So only choices are d or e

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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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VeritasPrepKarishma wrote:
Acer86 wrote:
12. 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

Try and reason out the answers logically if possible... that will give you a lot of confidence...
To understand the question, say
One mistake would have cost him 3 points : 49 points for correct answers, 2 points subtracted for 1 incorrect answer.
This means every one incorrect answer leads to a loss of 3 points.
Since he lost a total of 12 points, he must have had 4 questions incorrect.
So he must have answered 46 questions correctly.

Karishma
your way of handeling problems is awesome
this is infact real GMAT approach
hats off to you
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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A. 19-2(31) != 38
B. 38-2(12) !=38
C. 41-2(9) !=38
D. 44-2(6) !=38
E. 46-2(4) =38

Ans E.
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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Total questions: 50
Score per correct: 1
Total scores:50
Scores missed:50-38=12
Incorrect:12/2=6

Therefore, number of questions students answered correctly=50-6=44
I know the OA is E. Please explain.

thanks.
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Do you mean the answers like following?

A. 19-2(31) != -43, so it is wrong, because the score is 38.
B. 38-2(12) != 14, so it is wrong again.
C. 41-2(9) != 23, so it is wrong
D. 44-2(6) != 32, wrong.
E. 46-2(4) =38, correct because that's the score.

A. 19-2(31) != 38
B. 38-2(12) !=38
C. 41-2(9) !=38
D. 44-2(6) !=38
E. 46-2(4) =38

vinayreguri wrote:
A. 19-2(31) != 38
B. 38-2(12) !=38
C. 41-2(9) !=38
D. 44-2(6) !=38
E. 46-2(4) =38

Ans E.
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
if u need it the mathematical style

let c = no. of correct answers
w = no. of wrong answers.

we know total questions = 50

==> c+w = 50 => c = 50-w --------- (1)

the teacher removed 2 times wrong answers from correct answer and gave the score as 38

==> c - 2w = 38 ----------- (2)

substitute (1) in (2)

50 - w - 2w = 38 => 50 - 38 = 3 w

=> w = 4 Therefore no. of wrong ans = 4 which implies no. of right = 46, E
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Student got 38 points, he had to get well over 40 correct since if he got 40 he'd have gotten only 30 points. Test 44 and 46.

44 - 2*6 = 32 --> nope
46 - 2*4 = 38 --> yay
E
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
That's what I mean in my previous reply.

far257 wrote:
Student got 38 points, he had to get well over 40 correct since if he got 40 he'd have gotten only 30 points. Test 44 and 46.

44 - 2*6 = 32 --> nope
46 - 2*4 = 38 --> yay
E
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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let x be number of correct questions . => 50-x is the number of incorrect questions.

so the professor scored the questions as x + 2(50-x).

given x + 2(50-x) = 38

=> x= 46

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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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let x be no. of correct answers
since all questions are attempted

according to given conditions,

x-2*(50-x)=38
3x=138
x=46
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Acer86 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

Project PS Butler : Question #73

questions by subtracting 2 times the number of incorrect answers from the number of correct answers, this means
x - 2y = 38
x + y = 50(given)

50 - y - 2y = 38
y = 4

x = 46

E
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Acer86 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

Project PS Butler : Question #73

Let # of correct Q = C
# of incorrect Q = 50 - C

C - (50-C)*2 = 38
C - 100 + 2C = 38
3C = 138

C = 46

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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Acer86 wrote:
12. 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

Try and reason out the answers logically if possible... that will give you a lot of confidence...
To understand the question, say
One mistake would have cost him 3 points : 49 points for correct answers, 2 points subtracted for 1 incorrect answer.
This means every one incorrect answer leads to a loss of 3 points.
Since he lost a total of 12 points, he must have had 4 questions incorrect.
So he must have answered 46 questions correctly.

I find logical solutions easier to calculate. is it a good thing for a great score ? VeritasKarishma
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
Shrey9 wrote:
Acer86 wrote:
12. 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

Try and reason out the answers logically if possible... that will give you a lot of confidence...
To understand the question, say
One mistake would have cost him 3 points : 49 points for correct answers, 2 points subtracted for 1 incorrect answer.
This means every one incorrect answer leads to a loss of 3 points.
Since he lost a total of 12 points, he must have had 4 questions incorrect.
So he must have answered 46 questions correctly.

I find logical solutions easier to calculate. is it a good thing for a great score ? VeritasKarishma

If you can arrive at logical solutions quickly, it is great for GMAT.
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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Top Contributor
Acer86 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

STRATEGY: As with all GMAT Problem Solving questions, we should immediately ask ourselves, Can I use the answer choices to my advantage?
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.

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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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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Re: An instructor scored a students test of 50 questions by subtracting 2 [#permalink]
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