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M05-25

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Bunuel
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M05-25 [#permalink] M05-25   16 Sep 2014, 00:25
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A candy manufacturer produces a range of candy types, consisting of 30% dark chocolate, 25% milk chocolate, 20% taffy, 5% caramel, and the remaining proportion of cream. Unfortunately, due to a hardware failure, the candy types got mixed up while wrapped. Before the factory detected the issue, they packed 80 boxes, each containing 20 individually wrapped candy pieces. What is the maximum number of candy pieces that a quality control inspector could unwrap and still not get a taffy candy?

A. 61
B. 320
C. 1279
D. 1280
E. 1281
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D
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Bunuel
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Re M05-25 [#permalink] M05-25   16 Sep 2014, 00:25
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A candy manufacturer produces a range of candy types, consisting of 30% dark chocolate, 25% milk chocolate, 20% taffy, 5% caramel, and the remaining proportion of cream. Unfortunately, due to a hardware failure, the candy types got mixed up while wrapped. Before the factory detected the issue, they packed 80 boxes, each containing 20 individually wrapped candy pieces. What is the maximum number of candy pieces that a quality control inspector could unwrap and still not get a taffy candy?

A. 61
B. 320
C. 1279
D. 1280
E. 1281


Since each box contains 20 individually wrapped candy pieces, the total number of candy pieces is:

80 boxes * 20 candy pieces per box = 1600 candy pieces.

Next, we need to calculate the number of taffy candies in the mix. We know that taffy makes up 20% of the total candy types, so the number of taffy candies is:

20% * 1600 candy pieces = 320 taffy candies.

Therefore, the maximum number of candy pieces that a quality control inspector could unwrap and still not get a taffy candy is:

1600 candy pieces - 320 taffy candies = 1280 candy pieces.


Answer: D
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Bunuel
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Re: M05-25 [#permalink] M05-25   12 Mar 2023, 04:44
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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kpop1234567890
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Re: M05-25 [#permalink] M05-25   16 Jan 2024, 12:48
Hi the proportion given to us initially of each candy refer to the proportion in total candies - how do we now the 1600 candies we are checking represent the total candies and not a sample of candies where proportions could be different?
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Re: M05-25 [#permalink] M05-25   16 Jan 2024, 15:18
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kpop1234567890
Hi the proportion given to us initially of each candy refer to the proportion in total candies - how do we now the 1600 candies we are checking represent the total candies and not a sample of candies where proportions could be different?
Bunuel

The problem assumes that the 1600 candies are a representative total, and the proportions of each candy type apply uniformly to this entire batch.
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Re: M05-25 [#permalink] M05-25   01 Aug 2024, 01:47
­I thought the question tried to be tricky and it might be like: After 1279 candies are unwrapped
- If the 1280th candy is a Taffy => We got a Taffy
- If the 1280th candy is not a Taffy => We can make sure that all the remaining are Taffy

But it seems I thought too much =))
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Re: M05-25 [#permalink]
01 Aug 2024, 01:47
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