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Which of two different jars, A and B, contain more candies?

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Which of two different jars, A and B, contain more candies?  [#permalink]

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New post 08 Jan 2018, 07:37
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Which of two different jars, A and B, contain more candies?

(1) The average (arithmetic mean) weight of the candies in jar A is 2.5 grams and the average weight of the candies in jar B is 2.8 grams.
(2) When the two jars are combined in a third jar, C, the average weight is 2.7 grams.

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Which of two different jars, A and B, contain more candies?  [#permalink]

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New post 08 Jan 2018, 10:40
Bunuel wrote:
Which of two different jars, A and B, contain more candies?

(1) The average (arithmetic mean) weight of the candies in jar A is 2.5 grams and the average weight of the candies in jar B is 2.8 grams.
(2) When the two jars are combined in a third jar, C, the average weight is 2.7 grams.


Statement 1: let jar A contain \(x\) candies and jar B contain \(y\) candies. So total weight of Jar A \(=2.5x\) & that of Jar B\(=2.8y\). But we do not have any relation connecting these two weights, hence \(x\) & \(y\) cannot be calculated. Insufficient

Statement 2: No information to calculate number of candies in Jar A & B. Insufficient

Combining 1 & 2: we have \(2.5x+2.8y=2.7(x+y) => \frac{y}{x}=\frac{2}{1}\). Hence Jar B has more candies. Sufficient

Option C
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Re: Which of two different jars, A and B, contain more candies?  [#permalink]

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New post 08 Jan 2018, 11:23
Bunuel wrote:
Which of two different jars, A and B, contain more candies?

(1) The average (arithmetic mean) weight of the candies in jar A is 2.5 grams and the average weight of the candies in jar B is 2.8 grams.
(2) When the two jars are combined in a third jar, C, the average weight is 2.7 grams.


Based on the first statement, we cannot really say which jar has more candles. Based on second statement alone also, there is nothing to be said.

But when we combine the two statements, we see that the net average (weighted average) is inclined more towards average of jar B than towards average of jar A (combined average weight of 2.7 grams is closer to the average weight of jar B 2.8 grams than that of jar A which is 2.5 grams). Thus there are definitely more candles in jar B than in jar A.

Hence C answer
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Re: Which of two different jars, A and B, contain more candies?  [#permalink]

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New post 08 Jan 2018, 19:17
C should be the answer IMO, assuming all the candies have same weight.
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Re: Which of two different jars, A and B, contain more candies?  [#permalink]

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New post 08 Jan 2018, 22:31
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NikMan wrote:
C should be the answer IMO, assuming all the candies have same weight.


Hi

Its not necessary for all candles to have the same weight. Whether the weights of candles are same or different, if the combined average weight of the two jars is closer to a particular jar - then that jar has got more candles.

You can refer to the solution by niks18 posted above, which explains this thing algebraically.
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Re: Which of two different jars, A and B, contain more candies?  [#permalink]

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New post 09 Jan 2018, 18:32
amanvermagmat wrote:
NikMan wrote:
C should be the answer IMO, assuming all the candies have same weight.


Hi

Its not necessary for all candles to have the same weight. Whether the weights of candles are same or different, if the combined average weight of the two jars is closer to a particular jar - then that jar has got more candles.

You can refer to the solution by niks18 posted above, which explains this thing algebraically.


@amanvermagmat- You are absolutely correct, the combined average will always sway towards the jar with the more candies. I also proved this with general weights acting alegbraically in a manner similar to niks18's.
Also, in retrospect, my statement above appears quite foolish. In case all the candies had the same weight, the average wt for all three bags would be that same wt only, irespective of the nos.
Thank-you very much for pointing this out.
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Re: Which of two different jars, A and B, contain more candies? &nbs [#permalink] 09 Jan 2018, 18:32
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Which of two different jars, A and B, contain more candies?

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