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M23-19

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Math Expert
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Joined: 02 Sep 2009
Posts: 58434
M23-19  [#permalink]

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New post 16 Sep 2014, 01:19
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

81% (01:24) correct 19% (02:11) wrong based on 193 sessions

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Mike has to take five tests containing 80 questions each. If after completing four tests, Mike has an average of 80 percent of correct answers, what is the least number of questions Mike needs to get right in the fifth test to bring his average to 82% ?

A. 70
B. 72
C. 75
D. 78
E. 80

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Re M23-19  [#permalink]

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New post 16 Sep 2014, 01:19
Official Solution:

Mike has to take five tests containing 80 questions each. If after completing four tests, Mike has an average of 80 percent of correct answers, what is the least number of questions Mike needs to get right in the fifth test to bring his average to 82% ?

A. 70
B. 72
C. 75
D. 78
E. 80


In order to answer the question, we need to know how many questions were answered correctly in the first four tests.

\(80*4=320\), \(320*80\%=256\)

Now we have to find out how many questions of all 400 questions from 5 tests need to be answered correctly so that the average of 82% is achieved:

\(400*82\%=328\)

Finding the difference between 328 and 256 we can answer the question of the problem:

\(328-256=72\)


Answer: B
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Concentration: Technology, Leadership
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M23-19  [#permalink]

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New post 03 Jul 2017, 07:35
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1
I guess this can be approached using the Alligation method as well. In case anyone interested, this is how I did it. Snapshot attached


From the Alligation we get

\(\frac{4}{1} = \frac{(x - 82)}{2}\)

\(8 = (x-82)\)

\(90 = x\)

Meaning mike has to get 90% questions right in his 5th attempt

=\((90/100) * 80 = 72\)


Final Answer : B

>> !!!

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Re: M23-19  [#permalink]

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New post 12 Mar 2018, 06:37
My approach was:

in previous 4 tests mike got 2% less in each. In the fifth test he should get 5 times 2% to increase the average % by 2.
80*80%=64
80*10%=8 Mikes current average score needs 8 points more to achieve 2% increase.

Does such approach make sense?
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Re: M23-19  [#permalink]

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New post 12 Mar 2018, 07:16
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Re: M23-19   [#permalink] 12 Mar 2018, 07:16
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