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# M23-19

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Math Expert
Joined: 02 Sep 2009
Posts: 52431

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16 Sep 2014, 00:19
00:00

Difficulty:

15% (low)

Question Stats:

82% (01:21) correct 18% (02:16) wrong based on 179 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

_________________
Math Expert
Joined: 02 Sep 2009
Posts: 52431

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16 Sep 2014, 00:19
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:

$$328-256=72$$

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Manager
Joined: 12 Jun 2016
Posts: 216
Location: India
WE: Sales (Telecommunications)

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03 Jul 2017, 06:35
1
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

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

>> !!!

You do not have the required permissions to view the files attached to this post.

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My Best is yet to come!

Manager
Joined: 13 Feb 2018
Posts: 151

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12 Mar 2018, 05:37
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?
Math Expert
Joined: 02 Sep 2009
Posts: 52431

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12 Mar 2018, 06:16
LevanKhukhunashvili wrote:
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?

______________
Absolutely.
_________________
Re: M23-19 &nbs [#permalink] 12 Mar 2018, 06:16
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# M23-19

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