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If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 2

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Bunuel
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If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 2 [#permalink] New post   23 Apr 2021, 02:45
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77% (01:47) correct 23% (02:21) wrong based on 35 sessions
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If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 26.5, what is the value of x?

(A) 25.5
(B) 17.6
(C) 13.2
(D) 12.1
(E) 12
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D
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Re: If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 2 [#permalink] New post   23 Apr 2021, 03:47
26.5 * 6 = 159 is the total sum of the set

Given that set consists of numbers with decimals and that the answer choices have differing decimal values, one can focus solely on them.

Adding up the given decimal values from the set: 0.5+0.3+0.8+0.7+0.6 = 2.9

As we know the total sum of the set has no decimals, x must be a value with the decimal .1

Answer D 12.1

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Re: If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 2 [#permalink] New post   23 Apr 2021, 04:09
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Solution

Given
    • Numbers: 25.5, 34.3, 30.8, 28.7, 27.6 and x
      o Average of the above numbers = 26.5

To find
    • The value of x

Approach and Working out:
    • Average of 25.5, 34.3, 30.8, 28.7, 27.6 and x = 26.5
      o Total numbers = 6
    • \(\frac{25.5 + 34.3 +30.8+ 28.7 + 27.6 +x }{6 }\)= 26.5
    • 25.5 + 34.3 +30.8+ 28.7 + 27.6 +x = 6 × 26.5
    • 25.5 + 34.3 +30.8+ 28.7 + 27.6 +x = 159
    • 146 .9 + x = 159
    • x = 12.1

Hence, option D is the correct answer.
Correct Answer: Option D
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If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 2 [#permalink] New post   23 Apr 2021, 05:00
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Solution:

The sum of differences of the elements from the mean is always 0


{For ex- If we have 1,2,3,4,5 and we replace every element with the mean of these 5 numbers that is 3 then the differences are -2,-1,0,1,2 and the sum of the differences is 0}

Deviation of the elements from the mean excluding x are (25.5-26.5) , (34.3-26.5) , (30.8 - 26.5),(28.7-26.5),(27.6-26.5)

= -1, 7.8 , 4.3 , 2.2 , 1.1

Sum of these differences = 14.4

So x must create -14.4 as a difference with 26.5 in order to make the sum of the deviation 0.

=> x = 26.5 - 14.4

=12.1 (option d)

Devmitra Sen
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If the average of the numbers 25.5, 34.3, 30.8, 28.7, 27.6 and x is 2 [#permalink]
23 Apr 2021, 05:00
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