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If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then

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If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then  [#permalink]

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New post 08 Aug 2019, 01:34
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79% (01:02) correct 21% (01:10) wrong based on 14 sessions

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Re: If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then  [#permalink]

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New post 08 Aug 2019, 03:51
Bunuel wrote:
If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?

A. 3
B. 15
C. 17
D. 35
E. 42


Given: If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17.

Asked: What is x?

If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17.
(8+12+15+21+x+11)/6 = 17
67+x=17*6 = 102
x=102-67 = 35

IMO D
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If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then  [#permalink]

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New post 08 Aug 2019, 04:55
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Bunuel wrote:
If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then what is x?

A. 3
B. 15
C. 17
D. 35
E. 42


As arithmetic mean is given we can solve using two ways.
1) By using algebra : sum of all elements = AM * Number of elements(8 + 12 + 15 + 21 + x + 11 = 17 * 6)
which gives x = 35

2) By taking difference of each element(including unknown) from Arithmetic mean and adding together equate to zero to find 'x'. The differences are a follows:
8 - 17 = -9
12 -17 = -5
15 - 17 = -2
21 - 17 = 4
x - 17
11 - 17 = -6

Now x - 17 + (-9) +(-5) + (-2) + (4) + (-6) = 0
 x - 17 -18 = 0
 x = 35

Answer (D)
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If the average arithmetic mean of 8, 12, 15, 21, x and 11 is 17 then   [#permalink] 08 Aug 2019, 04:55
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