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A student responded to all of the 22 questions on a test and

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A student responded to all of the 22 questions on a test and [#permalink] New post 27 Mar 2008, 18:17
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A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

A. 3
B. 4
C. 15
D. 18
E. 20
[Reveal] Spoiler: OA

Last edited by Bunuel on 01 Jul 2012, 01:39, edited 1 time in total.
Added the OA.
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Re: PS: test [#permalink] New post 27 Mar 2008, 18:27
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A-3

If x is the number of questions answered correctly...
3.5x - (22-x)*1 = 63.5
x = 19
So number of wrong answers=22-19=3
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Re: PS: test [#permalink] New post 27 Mar 2008, 18:38
sreehari wrote:
A-3

If x is the number of questions answered correctly...
3.5x - (22-x)*1 = 63.5
x = 19
So number of wrong answers=22-19=3


how did you come up with 3.5x - (22-x)*1 if it says that "by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer"???
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Re: PS: test [#permalink] New post 28 Mar 2008, 06:43
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el1981 wrote:
A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?
(A) 3
(B) 4
(C) 15
(D) 18
(E) 20


Let the number of correct answers be X
The number of incorrect answers will be 22-X
For each correct answer the student got 3.5 points for a total of 3.5X
For each incorrect answer one point was taken out which is equivalent to -(22-X)
The total he got for that was 63.5

So in short you have the following equation and solution.

3.5X-(22-X) = 63.5
3.5X-22+X = 63.5
4.5X = 63.5+22
4.5X = 85.5
4.5X/4.5 = 85.5/4.5
X = 19
So incorrect answers will be 22-X = 22-19 = 3.
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Re: PS: test [#permalink] New post 31 Mar 2008, 00:20
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el1981 wrote:
A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?
(A) 3
(B) 4
(C) 15
(D) 18
(E) 20

This question can be answered without solving.
Total has 0.5 at the end, so no of correct answers should be odd, in turn no of incorrect answers must be odd too. A & C are only possible answers. C would drop the score too low so answer must be A.
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Re: A student responded to all of the 22 questions on a test and [#permalink] New post 30 Jun 2012, 11:17
Hi,

what does ,,total has O,5´´ mean?

Thanks in advance
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Re: A student responded to all of the 22 questions on a test and [#permalink] New post 01 Jul 2012, 02:31
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Expert's post
yuyalm wrote:
Hi,

what does ,,total has O,5´´ mean?

Thanks in advance


Juaz uses the following approach:

A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?
(A) 3
(B) 4
(C) 15
(D) 18
(E) 20

We have that 3.5*x-1*y=63.5, where x and y are the # of correct and incorrect answers.

Notice that x must be odd number in order the sum (63.5) to have 5 as the tenths digit (if x=even then 3.5*x-1*y=integer). So, y=22-x=22-odd=odd. There are only two odd choices 3 and 15. y cannot be 15 since in this case the total score would be less than 63.5, so y=3.

Answer: A.

Hope it's clear.
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Re: A student responded to all of the 22 questions on a test and [#permalink] New post 20 Sep 2013, 04:09
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Re: A student responded to all of the 22 questions on a test and [#permalink] New post 26 Sep 2013, 10:44
el1981 wrote:
A student responded to all of the 22 questions on a test and received a score of 63.5. If the scores were derived by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer, how many questions did the student answer incorrectly?

A. 3
B. 4
C. 15
D. 18
E. 20



sol:

x+y=22
3.5X - y = 63.5

X=19 and y =3

But Bunuel's method is super crazy and fastest
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Re: PS: test [#permalink] New post 20 Nov 2013, 02:11
el1981 wrote:
sreehari wrote:
A-3

If x is the number of questions answered correctly...
3.5x - (22-x)*1 = 63.5
x = 19
So number of wrong answers=22-19=3


how did you come up with 3.5x - (22-x)*1 if it says that "by adding 3.5 points for each correct answer and deducting 1 point for each incorrect answer"???



When I was trying this question I didn't figured out this shortcut, so I took the long road:

Step 1. Tried 15 erros first + 7 correct → 7*3.5 < 63.5 » conclusion: must be more correct questions than 7.
Step 2. Tried 4 erros first + 18 correct → 18*3.5 < 63.5 » conclusion: must be more correct questions than 18.
The only answer is A.
Re: PS: test   [#permalink] 20 Nov 2013, 02:11
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