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The average of 5 numbers is 7. When 3 new numbers are added, the avera 22 Apr 2021, 07:45
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The average of 5 numbers is 7. When 3 new numbers are added, the average of the eight numbers is 8.5. The average of the three new numbers is:

(A) 11
(B) 8.5
(C) 7.75
(D) 7.5
(E) 7
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A
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The average of 5 numbers is 7. When 3 new numbers are added, the avera 22 Apr 2021, 08:10
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Bunuel
The average of 5 numbers is 7. When 3 new numbers are added, the average of the eight numbers is 8.5. The average of the three new numbers is:

(A) 11
(B) 8.5
(C) 7.75
(D) 7.5
(E) 7
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The answer is option A

Sum of 5 no.s = 7*5=35
sum of 8 no.s = 8.5*8=68

subtract both, we will get the sum of three no.s = 33/3 =11.. this is the average of 3 no. s
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The average of 5 numbers is 7. When 3 new numbers are added, the avera 23 Apr 2021, 07:44
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Not sure if this is a good approach, but the way I approached this question was by first looking at the answer choices.

A was the only viable solution to me, because all the other values were 8.5 or lower, and to increase the average to 8.5 from 7 the average of the 3 new numbers must be higher than that increased number. Is this logic flawed, or is this a good alternative thought process?

Posted from my mobile device
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The average of 5 numbers is 7. When 3 new numbers are added, the avera 26 Apr 2021, 02:09
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Given
    • The average of 5 numbers is 7.
    • When 3 new numbers are added, the average of the eight numbers is 8.5.

To find
    • The average of the three new numbers.

Approach and Working out:
    • The average of 5 numbers is 7.
      o Sum of 5 numbers = 7 × 5 = 35

    • When 3 new numbers are added, the average of the eight numbers is 8.5.
      o Sum of 8 numbers = 8 × 8.5 = 68
      o Sum of 5 numbers + sum of 3 new numbers = 68
      o 35 + sum of 3 new numbers = 68
      o sum of 3 new numbers = 68 – 35 = 33
        • Average of 3 number numbers = 33/3 = 11

Hence, option A is the correct answer.

Correct Answer: Option A
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The average of 5 numbers is 7. When 3 new numbers are added, the avera 03 Aug 2022, 20:24
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Theory

    ➡ Average or Arithmetic Mean = Sum of all the Values / Total Number of Values
    ➡ Sum of All the values = Average * Total Number of Values

The average of 5 numbers is 7

Average = \(\frac{Sum}{5}\) = 7
=> Sum of 5 numbers = 7*5 = 35

When 3 new numbers are added, the average of the eight numbers is 8.5

Let the Sum of these three numbers be S
=> Sum of all 8 numbers = Sum of these 3 numbers + Sum of 5 numbers = S + 35

Average = \(\frac{Sum}{8}\) = \(\frac{S + 35}{8}\) = 8.5
=> S + 35 = 8*8.5 = 68
=> S = 68 - 35 = 33

The average of the three new numbers

Average = \(\frac{Sum}{3}\) = \(\frac{33}{3}\) = 11

So, Answer will be A.
Hope it helps!

Watch the following video to Learn the Basics of Statistics

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The average of 5 numbers is 7. When 3 new numbers are added, the avera 06 Jan 2025, 06:19
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IMO, that's a viable approach given the answer choices.
rheche
Not sure if this is a good approach, but the way I approached this question was by first looking at the answer choices.

A was the only viable solution to me, because all the other values were 8.5 or lower, and to increase the average to 8.5 from 7 the average of the 3 new numbers must be higher than that increased number. Is this logic flawed, or is this a good alternative thought process?

Posted from my mobile device
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