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The store gave away an average (arithmetic mean) of 92 candies per bas

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Math Expert
Joined: 02 Sep 2009
Posts: 58465
The store gave away an average (arithmetic mean) of 92 candies per bas  [#permalink]

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09 Oct 2019, 00:01
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Difficulty:

75% (hard)

Question Stats:

50% (01:18) correct 50% (01:15) wrong based on 22 sessions

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The store gave away an average (arithmetic mean) of 92 candies per basket. In the red baskets there was an average of 84 candies, and in the white baskets, the average number was 96. What was the ratio of the number of white baskets to the number of red baskets at the store?

A. 1 : 1
B. 1 : 2
C. 2 : 1
D. 2 : 3
E. 3 : 1

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Joined: 20 Aug 2017
Posts: 36
Re: The store gave away an average (arithmetic mean) of 92 candies per bas  [#permalink]

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09 Oct 2019, 00:20
1
Bunuel wrote:
The store gave away an average (arithmetic mean) of 92 candies per basket. In the red baskets there was an average of 84 candies, and in the white baskets, the average number was 96. What was the ratio of the number of white baskets to the number of red baskets at the store?

A. 1 : 1
B. 1 : 2
C. 2 : 1
D. 2 : 3
E. 3 : 1

This is a case of weighted averages. We know that there are average 92 candies.
There are 84 red candies and 96 white candies. Now if the ratio had been equal then the average number of candies would have been 90.
This also implies that there are more number of white candies.
So, options A,B,D are eliminated.

Now, 96 is at a distance of 4 from 92 and 84 is at a distance of 8 from 92.

From here we get the ratio of 2:1 of white baskets to red baskets.

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Re: The store gave away an average (arithmetic mean) of 92 candies per bas  [#permalink]

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09 Oct 2019, 10:32
Bunuel wrote:
The store gave away an average (arithmetic mean) of 92 candies per basket. In the red baskets there was an average of 84 candies, and in the white baskets, the average number was 96. What was the ratio of the number of white baskets to the number of red baskets at the store?

A. 1 : 1
B. 1 : 2
C. 2 : 1
D. 2 : 3
E. 3 : 1

given info
we can say
84*red+96*white/(red+white) = 96
solve
w/ r = 8/4 ; 2:1
IMO C
Re: The store gave away an average (arithmetic mean) of 92 candies per bas   [#permalink] 09 Oct 2019, 10:32
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