SOLUTION: On a certain mcq test 5 points are awarded for each correct answer and 4 points are deducted for each incorrect or unanswered question. Zakia received a total score of 10 points on

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Question 1119148: On a certain mcq test 5 points are awarded for each correct answer and 4 points are deducted for each incorrect or unanswered question. Zakia received a total score of 10 points on the test has more than 100 questions how many questions are on the test?
I.110 II.114 III. 119
A) II
B) I,II,III
C) I,II
D) I
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Let x be the number of correct answers and y the number of incorrect answers. Then

(1) x%2By+=+n where n is the total number of questions; the problem asks us which of the numbers 110, 114, or 119 could be the value of n

(2) 5x-4y+=+10 her score, at 5 points for each correct answer and -4 points for each incorrect answer, was 10

x and y have to be whole numbers. So solve the pair of equations for one of the variables and determine which values of n will yield whole numbers for that variable. Multiply the first equation by 4 and add the two equations, eliminating y:

4x%2B4y=4n
5x-4y=10
9x+=+4n%2B10

Now substitute each of the three answer choices for n and see which of them yield whole numbers for x:
9x = 4(110)+10 = 450 --> yes; x = 50
9x = 4(114)+10 = 466 --> no
9x = 4(119)+10 = 486 --> yes; x = 54

Both 110 and 119 could be the total number of questions on the test.

So the question as you show it is flawed, because "I, III" is not one of the answer choices.