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Many questions have a missing average Example: #Score 83 70

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gmathopful
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Many questions have a missing average Example: #Score 83 70 [#permalink] New post   10 Apr 2007, 17:40
Many questions have a missing average
Example:

#Score 83 70 92 X 64
#Stdts 05 06 03 05 01

Average of 20 students is 78.
What is X?
Is there a easy of finding x ( kind of average of averages), other than multiplying individually,adding and finding out X.
There should be some simple of finding out the X.



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Re: Many questions have a missing average Example: #Score 83 70 [#permalink] New post   10 Apr 2007, 19:18
gmathopful wrote:
Many questions have a missing average
Example:

#Score 83 70 92 X 64
#Stdts 05 06 03 05 01

Average of 20 students is 78.
What is X?
Is there a easy of finding x ( kind of average of averages), other than multiplying individually,adding and finding out X.
There should be some simple of finding out the X.


i would do this way.

average = 78

#Score #Stdts
83 5
70 6
92 3
X 5
64 1

the last digits of each product = 5 + 6 + 6 + ... + 4 = 21

so the missing number must have 7 as the unit digit but it could be 77 or 87. since 87 is too high from 78 should be 77.
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Re: Many questions have a missing average Example: #Score 83 70 [#permalink] New post   11 Apr 2007, 05:28
Himalayan wrote:

the last digits of each product = 5 + 6 + 6 + ... + 4 = 21

so the missing number must have 7 as the unit digit but it could be 77 or 87. since 87 is too high from 78 should be 77.

Bold part is 0, hence sum is 16.
But on the other hand, if you subtract the last digit from the total score(78*20 = 390) that leads to a last digit which can be quickly looked up to be divisible by one of the answer options.

So, 390-16 = 384, one of the answer choice's last digit multiple should lead to last digit 4. I have to try this out on some other questions.
Thanks
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Re: Many questions have a missing average Example: #Score 83 70 [#permalink] New post   11 Apr 2007, 11:33
gmathopful wrote:
Many questions have a missing average
Example:

#Score 83 70 92 X 64
#Stdts 05 06 03 05 01

Average of 20 students is 78.
What is X?
Is there a easy of finding x ( kind of average of averages), other than multiplying individually,adding and finding out X.
There should be some simple of finding out the X.


An average of a set of averages is the weighted average sum of all the averages.

Solve for x where [(5x83)+(6x70)+(3x92)+(5xX)+(1x64)]/20 = 78
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Re: Many questions have a missing average Example: #Score 83 70 [#permalink] New post   11 Apr 2007, 12:57
Since the avarege is given = 78

83-78 = 5

70-78 = -8

92-78 = 14

64-78 = -14

x-78 = x-78 (leave it for now)

its easier to work with small numbers - to solve

(5*5) + (-8*6) + (14*3) + (-14*1) + (X-78)*5 = 0 (have to be 0)

25 - 48 + 42 -14 + (X-78)*5 = 0

5 + (X-78)*5 = 0

X - 78 = -1

X = 77

its still a long way but the risk for error is smaller :-D
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gmathopful
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Re: Many questions have a missing average Example: #Score 83 70 [#permalink] New post   14 Apr 2007, 16:13
thats a good one. I was looking for smaller number to multiply/add.
Its much simpler.
Thanks



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Re: Many questions have a missing average Example: #Score 83 70 [#permalink]
14 Apr 2007, 16:13
Moderator:
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Senior Moderator - Masters Forum
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