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# From a set of 100 numbers, half were selected to form group I, and 60

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Math Expert
Joined: 02 Sep 2009
Posts: 60480
From a set of 100 numbers, half were selected to form group I, and 60  [#permalink]

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20 Nov 2019, 00:47
00:00

Difficulty:

55% (hard)

Question Stats:

54% (02:23) correct 46% (02:38) wrong based on 26 sessions

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From a set of 100 numbers, half were selected to form group I, and 60 percent of the remaining numbers were selected to form group II. The average (arithmetic mean) of the numbers in group I is 24.4, and the average of the numbers in group II is 31.5. Which of the following is closest to the average of the numbers in groups I and II combined?

A. 27.1

B. 27.6

C. 27.8

D. 28.0

E. 28.3

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Joined: 18 Aug 2017
Posts: 5693
Location: India
Concentration: Sustainability, Marketing
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WE: Marketing (Energy and Utilities)
Re: From a set of 100 numbers, half were selected to form group I, and 60  [#permalink]

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20 Nov 2019, 01:30
group 1 = 50
avg = 24.4 ; sum = 1220
group II = 30
avg= 31.5 ; sum = 945
total sum = 1220+945 ; 2165
avg = 2165/80 = ~27.1
IMO A

Bunuel wrote:
From a set of 100 numbers, half were selected to form group I, and 60 percent of the remaining numbers were selected to form group II. The average (arithmetic mean) of the numbers in group I is 24.4, and the average of the numbers in group II is 31.5. Which of the following is closest to the average of the numbers in groups I and II combined?

A. 27.1

B. 27.6

C. 27.8

D. 28.0

E. 28.3
Senior Manager
Joined: 16 Feb 2015
Posts: 252
Location: United States
Concentration: Finance, Operations
Re: From a set of 100 numbers, half were selected to form group I, and 60  [#permalink]

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20 Nov 2019, 02:37
Bunuel wrote:
From a set of 100 numbers, half were selected to form group I, and 60 percent of the remaining numbers were selected to form group II. The average (arithmetic mean) of the numbers in group I is 24.4, and the average of the numbers in group II is 31.5. Which of the following is closest to the average of the numbers in groups I and II combined?

A. 27.1

B. 27.6

C. 27.8

D. 28.0

E. 28.3

Group 1: 1/2 of total i.e. 50
Group 2: 3/5 of remaining 50 i.e. 30

Avg. of Group 1: 24.4 , Avg. of Group 2: 31.5

New Avg = { (24.4*50) + (31.5*30) } / 80
= 27.0625 = 27.1 (aprox.) Option A is Answer

Please give kudos, if you find my explanation good enough
Re: From a set of 100 numbers, half were selected to form group I, and 60   [#permalink] 20 Nov 2019, 02:37
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