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Math Expert V
Joined: 02 Sep 2009
Posts: 55804
On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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3 00:00

Difficulty:   45% (medium)

Question Stats: 72% (01:59) correct 28% (02:09) wrong based on 151 sessions

HideShow timer Statistics 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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Intern  B
Joined: 17 Aug 2016
Posts: 48
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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1
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)
Intern  Joined: 17 Apr 2016
Posts: 4
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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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.

Sent from my SM-G130H using GMAT Club Forum mobile app
Current Student B
Joined: 26 Jan 2016
Posts: 100
Location: United States
GPA: 3.37
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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1
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
Manager  Joined: 29 Aug 2008
Posts: 106
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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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.

Option B.
Manager  Joined: 17 Nov 2013
Posts: 80
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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1
9c - 7i = 0
9c = 7i
c = 7i/9

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

t = 16, 32, 48

VP  P
Joined: 31 Oct 2013
Posts: 1376
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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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.

e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2911
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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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.

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Intern  B
Status: No Progress without Struggle
Joined: 04 Aug 2017
Posts: 42
Location: Armenia
GPA: 3.4
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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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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Seryozha Sargsyan 21

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Intern  Joined: 30 Aug 2018
Posts: 1
Re: On a certain multiple-choice test, 9 points are awarded for each corre  [#permalink]

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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? Re: On a certain multiple-choice test, 9 points are awarded for each corre   [#permalink] 16 Sep 2018, 00:51
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