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While exploring a cave, Carl comes across a collection of 5-pound rock 08 Dec 2018, 09:58
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C
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55% (hard)

Question Stats:

67% (02:24) correct 33% (02:24) wrong based on 129 sessions

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While exploring a cave, Carl comes across a collection of 5-pound rocks worth 14 each, 4-pound rocks worth 11 each, and 1-pound rocks worth 2 each. There are at least 20 of each size. He can carry at most 18 pounds. What is the maximum value, in dollars, of the rocks he can carry out of the cave?

A) 48
B) 49
C) 50
D) 51
E) 52
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C
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While exploring a cave, Carl comes across a collection of 5-pound rock 08 Dec 2018, 10:10
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4 x 4-lb = $44
2 x 1-lb = $4
Total weight = 18-lb
Total value = $48
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While exploring a cave, Carl comes across a collection of 5-pound rock 08 Dec 2018, 12:59
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w/ a maximum of 18 lbs he carry double load of the 1st & 2nd kind, which means total cost will be 2*14 + 2*11 = 50. Answer C.
Total Load in lbs will be 2*5 + 2*4 = 18
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While exploring a cave, Carl comes across a collection of 5-pound rock 09 Dec 2018, 07:20
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We have 5-pound rocks worth 14 each, 4-pound rocks worth 11 each, and 1-pound rocks worth 2 each.
So, value per pound of 5 pound rock = 14/5 = 2.8
value per pound of 4 pound rock = 11/4 = 2.75
value per pound of 1 pound rock = 2/1 = 2

Now we need total of 18 pound maximum.. So, we can start making combination having rocks which has max. value per pound.

So, this can be done in following ways.
1. 3 five pound rock + 3 two pound rock: Total weight = 18 pound , Total value = 14x3 + 2x3 = 48
2. 4 four pound rock + 2 two pound rock: Total weight = 18 pound, Total value = 11x4 + 2x2 = 48

So, the maximum value, in dollars, of the rocks he can carry out of the cave. = 48 dollars.

Answer A
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While exploring a cave, Carl comes across a collection of 5-pound rock 09 Dec 2018, 08:02
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The dollar per pound is greatest for the 5 pound rock, then the 4 pound and lastly for the 1 pound. So we should take:
Two 5 pound rocks =2*$14= 28
Two 4 pound rocks= 2*$11= 22
Total weight: 50
IMO answer is option C

P.S: We need to find the maximum value, in dollars, of the rocks he can carry out of the cave. That is why I took 5lb and 4lb rock.
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While exploring a cave, Carl comes across a collection of 5-pound rock 10 Dec 2018, 07:12
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Official Explanation



The ratio of dollar per pound is greatest for the 5 pound rock, then the 4 pound, lastly the 1 pound. So we should take two 5 pound rocks and two 4 pound rocks. Total weight: 2*14 +2*11 =50
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While exploring a cave, Carl comes across a collection of 5-pound rock 09 Oct 2025, 03:42
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