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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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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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.

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

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

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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