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

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Math Expert
Joined: 02 Sep 2009
Posts: 56307
The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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29 Mar 2018, 00:14
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Difficulty:

15% (low)

Question Stats:

91% (01:16) correct 9% (02:43) wrong based on 48 sessions

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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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Joined: 20 Aug 2016
Posts: 17
Location: India
WE: Operations (Computer Software)
The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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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

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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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29 Mar 2018, 14:34
A

110K + 110 = 100K + 180,
K = 7
Target Test Prep Representative
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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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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

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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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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
Intern
Joined: 19 Jan 2017
Posts: 1
The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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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)
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 2943
Re: The mean of a list of K numbers is 100. If the number 180 is appended  [#permalink]

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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.

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