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

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Manager
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A student responded to all of the 22 questions on a test and [#permalink]

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27 Mar 2008, 19:17
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Difficulty:

35% (medium)

Question Stats:

70% (01:38) correct 30% (01:48) wrong based on 775 sessions

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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, 02:39, edited 1 time in total.

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27 Mar 2008, 19:27
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A-3

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

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27 Mar 2008, 19:38
sreehari wrote:
A-3

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

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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28 Mar 2008, 07:43
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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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31 Mar 2008, 01:20
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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]

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30 Jun 2012, 12:17
Hi,

what does ,,total has O,5´´ mean?

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Re: A student responded to all of the 22 questions on a test and [#permalink]

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01 Jul 2012, 03:31
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yuyalm wrote:
Hi,

what does ,,total has O,5´´ mean?

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.

Hope it's clear.
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Re: A student responded to all of the 22 questions on a test and [#permalink]

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20 Sep 2013, 05:09
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Re: A student responded to all of the 22 questions on a test and [#permalink]

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26 Sep 2013, 11:44
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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20 Nov 2013, 03:11
el1981 wrote:
sreehari wrote:
A-3

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

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.

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Re: A student responded to all of the 22 questions on a test and [#permalink]

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07 Dec 2014, 13:58
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Re: A student responded to all of the 22 questions on a test and [#permalink]

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03 Feb 2016, 06:31
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Re: A student responded to all of the 22 questions on a test and [#permalink]

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31 Mar 2017, 10:42
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Re: A student responded to all of the 22 questions on a test and [#permalink]

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31 Mar 2017, 13:29
If he answered 3 wrong then he got 19 correct
19 x 3.5 = 66.3 - 3 = 63.5

No need to work out the other four answers

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Re: A student responded to all of the 22 questions on a test and   [#permalink] 31 Mar 2017, 13:29
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