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A test has 200 questions. Each question has 5 options, but only 1

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A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post Updated on: 09 Apr 2015, 06:34
3
15
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

51% (02:36) correct 49% (02:47) wrong based on 120 sessions

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A test has 200 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?

A. 31
B. 33
C. 35
D. 40
E. 42

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Originally posted by Lucky2783 on 09 Apr 2015, 03:22.
Last edited by Bunuel on 09 Apr 2015, 06:34, edited 1 time in total.
Renamed the topic, edited the question, added the OA and moved to PS forum.
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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 09 Apr 2015, 04:02
3
1
Lucky2783 wrote:
A test has 200 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point.
However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted.
A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40.
What is the maximum possible number of such test-takers?

A. 31
B. 33
C. 35
D. 40
E. 42


First variant - 40 answers right
Second variant 41 right and 4 wrong = 45 questions
Third variant 42 right and 8 wrong = 50 questions

And we see sequence of numbers that are multiple of 5

So we need to calculate quantity of numbers mulitple of 5 between 45 and 200 inclusive
(200-45)/5 = 31 + 1 = 32 variants + variant 40 answers right
33 variants

Answer is B
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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 09 Apr 2015, 14:57
Hi All,

This question has a great "brute force" element and pattern to it. Harley1980's approach to list out the first couple of "options" is a good way to start this question. The pattern he discovered can be used in a couple of different ways:

A correct answers get you 1 point, an incorrect answer gets you MINUS 1/4 point and a skipped question gets you 0 points. Since there are 200 total questions, there are a variety of ways to get a total of 40 points....

40 correct, 0 incorrect, 160 skipped
41 correct, 4 incorrect, 155 skipped
42 correct, 8 incorrect, 150 skipped
Etc.

To find all of the options, you can either "count up" (40+0 = 40, 41+4 =45, 42+8 = 50, etc.) OR you can "count down" from the number of skipped questions. (160, 155, 150, etc.). With either option, you'll eventually run out of questions, then you'll be done.

Counting down from 160 is probably faster, as long as you don't forget the final option - the one with 0 skipped questions). Here, there are 33 multiples of 5 (including the 0
'option').

Final Answer:

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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 10 Apr 2015, 04:13
3
The goal is to score only 40 by varying the number of questions answered correctly

Minimum correctly answered questions
First, answer the first 40 questions correct = 40 (leave out the rest)

Maximum correctly answered questions
we can equate the remaining 160 questions to nullify for each correct answer (1 correct answer – 4 * incorrect answer = 0 )
correct answer: 4 incorrect answers
x:4x = 160 (the remaining questions)
5x = 160
x = 32, (we can answer 72 questions correct, and nullify the 32 correct answers by answering the remaining 128 questions incorrect)

So number of variants = (72 max- 40 min ) + 1 = 33
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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 10 Jan 2016, 19:46
picked at random, and luckily correct...tough one..but the methods above are making this question a very easy one...
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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 02 Sep 2016, 12:53
Excellent question...loved solving it, but took close to 4:30mins ...sighhhh
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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 03 Sep 2016, 15:21
Hi vabhs192003,

What approach did you use? As a general rule, you won't come across any Quant questions on Test Day that 'require' more than about 3 minutes of work, so if 'your way' of answering the question takes a long time, then it's likely that there are other, faster and more efficient methods available.

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Re: A test has 200 questions. Each question has 5 options, but only 1  [#permalink]

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New post 30 Apr 2018, 21:17
Lucky2783 wrote:
A test has 200 questions. Each question has 5 options, but only 1 option is correct. If test-takers mark the correct option, they are awarded 1 point. However, if an answer is incorrectly marked, the test-taker loses 0.25 points. No points are awarded or deducted if a question is not attempted. A certain group of test-takers attempted different numbers of questions, but each test-taker still received the same net score of 40. What is the maximum possible number of such test-takers?

A. 31
B. 33
C. 35
D. 40
E. 42


In the question stem, we get the following details:
1. For every correct answer, the test-taker is awarded +1
2. For every mistake made, the test-taker will lose -0.25
3. For every question unattempted, the test-taker is neither awarded nor loses a point.

If the test-taker attempts 40 questions and get all of them right he will score 40.
In this scenario, he will not attempt the remaining 160 questions.

To test the maximum scenario,
If x is the number of questions the test-taker gets correctly,
then 200-x is the number of questions he gets wrong

\(x - 0.25(200-x) = 40\) -> \(x - 50 + 0.25x = 40\) -> \(1.25x = 90\) -> \(x = \frac{90}{1.25} = 72\)

The maximum number of questions he can get right to score 40 is x=72. Here, each of the
possibilities between 40 questions correct and 72 questions correct can result in a score of 40.

Therefore, the maximum possible number of such test-takers is \(72-40+1\) or 33(Option B)
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Re: A test has 200 questions. Each question has 5 options, but only 1 &nbs [#permalink] 30 Apr 2018, 21:17
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