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# M05-25

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Math Expert
Joined: 02 Sep 2009
Posts: 58320

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16 Sep 2014, 00:25
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Difficulty:

55% (hard)

Question Stats:

67% (02:26) correct 33% (02:43) wrong based on 200 sessions

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A candy factory manufactures various types of candy: 30% are dark chocolate, 25% are milk chocolate, 20% taffy, 5% caramel, and the rest are cream. Due to a hardware failure, all of the candy are mixed and dispatched into boxes holding 20 individually wrapped pieces of candy each. If 80 boxes are packed before the failure is caught, what is the maximum number of candy pieces a quality control inspector can open to get a taffy candy?

A. 61
B. 120
C. 800
D. 1281
E. 1321

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Math Expert
Joined: 02 Sep 2009
Posts: 58320

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16 Sep 2014, 00:25
4
Official Solution:

A candy factory manufactures various types of candy: 30% are dark chocolate, 25% are milk chocolate, 20% taffy, 5% caramel, and the rest are cream. Due to a hardware failure, all of the candy are mixed and dispatched into boxes holding 20 individually wrapped pieces of candy each. If 80 boxes are packed before the failure is caught, what is the maximum number of candy pieces a quality control inspector can open to get a taffy candy?

A. 61
B. 120
C. 800
D. 1281
E. 1321

There are total of $$20*80=1,600$$ candy pieces in 80 boxes. The worst case scenario would be if the inspector opens only candy which are not taffy. Since there are $$20\%*1,600=320$$ taffy then there are $$1,600-320=1,280$$ candy pieces, which are not taffy, so the maximum number of candy pieces the inspector needs to open to get a taffy candy is 1,281.

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Joined: 02 Jun 2016
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GMAT 1: 660 Q44 V36
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15 Dec 2017, 03:21
2
The question wording is a bit vague. For the logic used to solve this problem, shouldn't the question have stated "what is the maximum number of candy pieces a quality control inspector can open before he gets a taffy candy?".

Or, it should state, "gets only one taffy candy".

Otherwise, if it's just a case of getting "a" taffy candy, he can open all the 1600 candies, and still satisfy the condition. He can open 1281 and get a taffy candy or he can open 1600 and get a taffy candy for sure.
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Joined: 20 Dec 2017
Posts: 35
Location: Singapore

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03 Jul 2018, 22:18
I agree, I think this question is very confusing.

"what is the maximum number of candy pieces a quality control inspector can open to get a taffy candy?"

I interpreted the question as how many taffy candies are there in the 80 boxes. Since there are 320 taffy candies in the 1600 candies, the inspector can open a maximum of 320 candies to get a taffy candy.
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Joined: 11 Jun 2018
Posts: 98
Schools: DeGroote "22 (S)
GMAT 1: 500 Q39 V21

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18 Jan 2019, 08:47
@Bunuel:-hi Bunuel, for statements like these:-"what is the maximum number of candy pieces a quality control inspector can open to get a taffy candy?" , Are there any specific keywords that can reduce the confusion, because it really is very confusing.
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Joined: 01 Jan 2019
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25 May 2019, 04:06
Although I completely agree with the explaination, however, I have an issue with the wording of the question which states that " Due to a hardware failure, 20 boxes were mixed" & "80 were done before the failure was caught". Now these two statements indicate that 80 boxes were organized with candieand then a failure occurred and the remaining boxes were mixed up candies 20 each.

Also, what would be the case if it were asked that "what is the minimum number of candy pieces that the inspector can open to find taffy"?
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Joined: 09 Jun 2018
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11 Sep 2019, 11:48
I worked this out the long way, posting here in case it helps anyone.

_____________Dark Choc_____Milk Choc_____Taffy_____Caramel_____Cream
Percent_________30%__________25%_______20%_______5%_______20%_
# In 1 Box_______6_____________5__________4_________1_________4___
# In 80 Boxes___480___________400________320________80________320_

Since we're being asked about the maximum number of pieces an inspector would need to open to get a taffy candy out of the 80 boxes, we need to add the total number of Dark Chocolate candies, Milk Chocolate candies, Caramel candies, and Cream candies.

480+400+320+80 = 1280

Since 1280 is the total number of candies that are not taffy, the inspector would need to open an additional candy to ensure they opened a taffy candy.

1280+1 = 1281

Re: M05-25   [#permalink] 11 Sep 2019, 11:48
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# M05-25

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