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An instructor scored a student’s test of 50 questions by subtracting 2

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An instructor scored a student’s test of 50 questions by subtracting 2 [#permalink]

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New post 16 Mar 2011, 10:05
1
2
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

92% (00:45) correct 8% (00:59) wrong based on 38 sessions

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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
Spoiler: OA
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Re: An instructor scored a student’s test of 50 questions by subtracting 2 [#permalink]

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New post 16 Mar 2011, 10:21
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 16 Mar 2011, 18:17
1
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
Had the student answered all correctly, he would have scored 50.
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.
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Re: An instructor scored a student’s test of 50 questions by subtracting 2 [#permalink]

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New post 16 Mar 2011, 19:06
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 17 Mar 2011, 02:20
x - #of correct answers
y - # of incorrect answers

x + y = 50
x - 2y = 38

so 3y = 12 => y = 4, so x = 46.

Answer is E.
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Re: An instructor scored a student’s test of 50 questions by subtracting 2 [#permalink]

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New post 30 Mar 2011, 04:24
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
Had the student answered all correctly, he would have scored 50.
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 :thanks :beer
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Re: An instructor scored a student’s test of 50 questions by subtracting 2 [#permalink]

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New post 07 Aug 2011, 07:21
1
Try plugin answers
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 08 Aug 2011, 17:59
Total questions: 50
Score per correct: 1
Total scores:50
Scores received:38
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 08 Aug 2011, 22:24
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.

Does your explaination mean above?

Try plugin answers
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:
Try plugin answers
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 09 Aug 2011, 10:34
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 09 Aug 2011, 13:12
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 09 Aug 2011, 20:18
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 student’s test of 50 questions by subtracting 2 [#permalink]

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New post 21 Aug 2011, 20:08
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

Answer is E.
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Re: An instructor scored a student’s test of 50 questions by subtracting 2 [#permalink]

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New post 21 Aug 2011, 23:26
let x be no. of correct answers
since all questions are attempted
no. of incorrect answers =50-x

according to given conditions,

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

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Re: An instructor scored a student’s test of 50 questions by subtracting 2   [#permalink] 06 Oct 2017, 22:38
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