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On a certain multiple-choice test, 9 points are awarded for each corre

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On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 26 Oct 2016, 05:47
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On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?

A. Cannot be determined
B. 16
C. 19
D. 21
E. 24

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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 26 Oct 2016, 06:17
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9x - 7y = 0
x = 7/9 y --> y needs to be a multiple of 9 i.e 9, 18, 27 etc if y=9 x=7 if y=18 x=14 (18+14>30) therefore answer is 9+7 = 16 (B)
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 26 Oct 2016, 07:21
Let x be no. of correct questions and y be no. of incorrect or unaswered question.
9x-7y=0
9(7)-7(9)=0
therefore total number of questions on test =7+9=16
Ans:16

I hope i'm right.

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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 26 Oct 2016, 09:22
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The LCM of 7 and 9 is 63. In order to get a score of 0 she needs to get 7 question right (63 points) and 9 questions wrong (-63 points) to get a score of 0. 9+7=16
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 26 Oct 2016, 09:24
1
9x - 7y = 0

x + y < 30

9x = 7y

Y = 9x/7

So x has to be a multiple of 7 (7, 14, 21.....)

if X = 7 we get y =9 and the total no of questions as 16.

If we take x = 14, we get Y = 18 and total no of questions as 32, whereas we have been told that they are less than 30.

So 16 is the answer.

Option B.
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 24 Nov 2016, 07:58
1
9c - 7i = 0
9c = 7i
c = 7i/9

i = 9, 18, 27
c = 7, 14, 21

t = 16, 32, 48

answer is B
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 18 Jul 2018, 14:33
Bunuel wrote:
On a certain multiple-choice test, 9 points are awarded for each correct answer, and 7 points are deducted for each incorrect or unanswered question. Sally received a total score of 0 points on the test. If the test has fewer than 30 questions, how many questions are on the test?

A. Cannot be determined
B. 16
C. 19
D. 21
E. 24



Let the number of correct question be x

and the number of incorrect question be y.

Note : As final result is 0, it's clear that marks from correct answer and the marks from incorrect answer were same.

So,

9x = 7y

x/y = 7 / 9

( x + y ) = 16 or the multiple of 16.

As total question is less than 30, it's clear that total number of questions was 16.

The best answer is B.
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 19 Jul 2018, 05:02

Solution



Given:
• In the test, 9 points are awarded for each correct answer.
• Else, 7 points are deducted
• Sally received a total score of 0 points on the test
• The test has fewer than 30 questions

Approach and Working:
Let, the correct question be x and rest questions be y.
Hence, 9x-7y=0
• x=7, y=9, x+y= 16
• x= 14, y= 18 , x+y= 32
• and more..
• But, there is only one possible value of x and y such that x+y is less than 30.
Hence, the correct answer is option B.

Answer: B
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 29 Jul 2018, 06:57
We should firstly write an appropriate equation. Let's assign r for the number of right questions and w for the number of wrong questions.
So, 9r-7w=0
9r=7w
w=9r/7
So, r has to be a multiple of 7.
From the multiples of 7, only 7 satisfies the equation since the number of questions should not surpass 30.
7+9=16
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Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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New post 15 Sep 2018, 23:51
No test will give you result in negative. You either score a zero or more. So, even if the girl has written every answer wrongly - the score would be still 0. 16 is another possibility. So the answer should be CAN'T BE DETERMINED right? How is it selected as 16?
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Re: On a certain multiple-choice test, 9 points are awarded for each corre &nbs [#permalink] 15 Sep 2018, 23:51
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