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22 Jun 2021, 08:15
Kudos
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
25%
(medium)
Question Stats:
82% (02:03) correct
18%
(02:10)
wrong
based on 119
sessions
History
Date
Time
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Not Attempted Yet
A student took a test in which 3 marks were given for each correct answer and 0.5 marks were deducted for an incorrect answer. If the test had 25 questions and the student attempted all the questions and got 40 marks in total, what is the difference between the number of correct and incorrect answers?
(A) 5
(B) 10
(C) 12
(D) 15
(E) 18
(A) 5
(B) 10
(C) 12
(D) 15
(E) 18
22 Jun 2021, 08:29
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Explanation:
Let wrong number of questions are x
Correct number of questions are 25-x
(25-x)*3 + (-0.5)*x = 40
75 - 3x -0.5x = 40
35 = 3.5x
x = 35/3.5
x = 10
Wrong Question = 10
Correct Question = 15
Difference = 15-10 = 5
IMO-A
Posted from my mobile device
Let wrong number of questions are x
Correct number of questions are 25-x
(25-x)*3 + (-0.5)*x = 40
75 - 3x -0.5x = 40
35 = 3.5x
x = 35/3.5
x = 10
Wrong Question = 10
Correct Question = 15
Difference = 15-10 = 5
IMO-A
Posted from my mobile device
22 Jun 2021, 08:51
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Algebra works well here, as explained in the post above. There are other ways to solve too:
The sum of the number of correct answers and the number of incorrect answers is 25, which is odd, so the difference of those two numbers will also be odd (if x+y is odd, so is x-y, when x and y are integers). Answer D, 15, is way too large (that would mean 20 right and 5 wrong answers, but then the test taker will get almost 60 points), so the answer must be B.
Or you might notice that the penalty for wrong answers is very small. To get 40 points, a test taker certainly needs more than 13 right answers (13*3 is less than 40), but since the wrong answer penalty has only a small effect, the test taker getting 40 points exactly will have approximately 14 or 15 right answers (and roughly 11 or 10 wrong answers), so the difference won't be very big and the only plausible difference among the choices is 5. Of course, at this point, it's also not much work to confirm that the test taker has exactly 15 right answers and 10 wrong answers.
The sum of the number of correct answers and the number of incorrect answers is 25, which is odd, so the difference of those two numbers will also be odd (if x+y is odd, so is x-y, when x and y are integers). Answer D, 15, is way too large (that would mean 20 right and 5 wrong answers, but then the test taker will get almost 60 points), so the answer must be B.
Or you might notice that the penalty for wrong answers is very small. To get 40 points, a test taker certainly needs more than 13 right answers (13*3 is less than 40), but since the wrong answer penalty has only a small effect, the test taker getting 40 points exactly will have approximately 14 or 15 right answers (and roughly 11 or 10 wrong answers), so the difference won't be very big and the only plausible difference among the choices is 5. Of course, at this point, it's also not much work to confirm that the test taker has exactly 15 right answers and 10 wrong answers.
