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The mean of a list of K numbers is 100. If the number 180 is appended

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The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 29 Mar 2018, 00:14
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The mean of a list of K numbers is 100. If the number 180 is appended to the list of K numbers, the new list of K + 1 numbers has a mean of 110. What is the value of K?

(A) 7
(B) 9
(C) 10
(D) 18
(E) 30

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The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 29 Mar 2018, 01:00
The mean of a list of K numbers is 100. If the number 180 is appended to the list of K numbers, the new list of K + 1 numbers has a mean of 110. What is the value of K?

(A) 7
(B) 9
(C) 10
(D) 18
(E) 30

K number in the list as given in the question.

now as we know mean = sum of the all elements of list / Number of elements

so 100 = sum of the all elements of list / K

==> sum of the all elements of list = 100K

Now we are adding 180 to the list so there are K+1 element now.

New mean = (sum of the all elements of list + 180) / (K+1)

so 110 = (100k+180) / (K+1)

110(K+1) = 100K+ 180

solving the above equation we get

110K + 110 = 100 K + 180
10K = 70
K = 7

Answer is A
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Re: The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 29 Mar 2018, 14:34
A

110K + 110 = 100K + 180,
K = 7
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Re: The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 30 Mar 2018, 10:56
Bunuel wrote:
The mean of a list of K numbers is 100. If the number 180 is appended to the list of K numbers, the new list of K + 1 numbers has a mean of 110. What is the value of K?

(A) 7
(B) 9
(C) 10
(D) 18
(E) 30


Since mean x number = sum, we see that the sum of the K numbers is 100K. When 180 is added to the list we use the formula: sum/number = mean, and we have:

(100K + 180)/(K + 1) = 110

100K + 180 = 110(K + 1)

100K + 180 = 110K + 110

70 = 10K

7 = K

Answer: A
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Re: The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 31 Mar 2018, 12:04
Bunuel wrote:
The mean of a list of K numbers is 100. If the number 180 is appended to the list of K numbers, the new list of K + 1 numbers has a mean of 110. What is the value of K?

(A) 7
(B) 9
(C) 10
(D) 18
(E) 30


let t=total of K numbers
t=100K
t=110*(K+1)-180
➡t=110K-70
thus, 100K=110K-70
K=7
A
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The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 04 Apr 2018, 00:33
If 100 was added to the list the average would have remained 100 itself but since 180 is added which 80 in excess and so average is increased by 10 so
to find the list of numbers we do,
80/10=8
which represent the new list.
old list=8-1=7
hence option(A)
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Re: The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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New post 04 Apr 2018, 02:38

Solution



Given:
    • The mean of the list K numbers is 100.
    • When 180 is added to the list, the mean becomes 110.

To find:
    • What is the value of K?

Approach and Working out:

    • The mean of K numbers is 100.
      o Sum of K numbers/ K= 100
      o Sum of K numbers= 100* K ---------- (1)

    • The mean when 180 is appended to the list of K numbers, the mean becomes 110.
      o (Sum of K number+180)/ (K+1) = 110
      o 100K+180= 110 K+110
      o 10K= 70
      o K=7

Thus, the value of K is 7.

Hence, the correct answer is option A.

Answer: A

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Re: The mean of a list of K numbers is 100. If the number 180 is appended &nbs [#permalink] 04 Apr 2018, 02:38
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