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A teacher scored a student's test of 30 questions by subtracting 2 tim

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Manager
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Joined: 30 May 2018
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GMAT 1: 620 Q42 V34
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A teacher scored a student's test of 30 questions by subtracting 2 tim  [#permalink]

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New post 20 Apr 2019, 03:04
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

56% (01:47) correct 44% (01:29) wrong based on 32 sessions

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A teacher scored a student's test of 30 questions by subtracting 2 times the number of incorrect answers from the number of correct answers. If the student answered all of the questions, which of the following could be the score the student received?

I. 15
II. 18
III. 25

A. I only
B. II only
C. III only
D. I and II
E. I and III
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A teacher scored a student's test of 30 questions by subtracting 2 tim  [#permalink]

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New post 20 Apr 2019, 19:21
1
I created a table
G W
30 - 0
29 - 1 = 2*1 = 2 = 27
28 - 2 = 2*2 = 4 = 24
27 - 3 = 2*3 = 6 = 21
26 - 4 = 2*4 = 8 = 18
25 - 5 = 2*5 = 10 = 15
24 - 6 = 2*6 = 12 = 12

As you can see, just multiples of 3 can be the right ones.

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A teacher scored a student's test of 30 questions by subtracting 2 tim  [#permalink]

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New post 20 Apr 2019, 03:12
I chose B but it says answer is D.
How is 15 possible. I have considered following points
1. An answer is either right or wrong. Number is always an integer
2. Subtract twice incorrect answers so subtracted value is always even

Hence 30(even) - even = even
So only possible answer from given options is 18 which is even

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Joined: 08 Apr 2019
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Re: A teacher scored a student's test of 30 questions by subtracting 2 tim  [#permalink]

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New post 20 Apr 2019, 03:29
If the student has marked 25 questions correct then score is 25-5*2=15

If 26 correct answers then score is 26-4*2=18

Similarly for 27 correct answers score will be 21 and the next possible scores will be 24 27 with a common difference of 3. So 25 can't be a valid score.

Hence option D

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Re: A teacher scored a student's test of 30 questions by subtracting 2 tim  [#permalink]

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New post 20 Apr 2019, 07:57
Let, X=total number of correct answers
30-X=total number of incorrect answers

So, Number obtained = X- 2(30-X)=3X-60
So, number obtained has to be a multiple of 3 minus 60.
I and II are satisfactory under the condition.
So, answer is D.
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Re: A teacher scored a student's test of 30 questions by subtracting 2 tim   [#permalink] 20 Apr 2019, 07:57
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