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A restaurant pays a seafood distributor d dollars for 6

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A restaurant pays a seafood distributor d dollars for 6  [#permalink]

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New post 27 Jan 2012, 14:27
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A
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C
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A restaurant pays a seafood distributor d dollars for 6 pounds of Maine lobster. Each pound can make v vats of lobster bisque, and each vat makes b bowls of lobster bisque. If the cost of the lobster per bowl is an integer, and if v and b are different prime integers, then which of the following is the smallest possible value of d?
(A) 15
(B) 24
(C) 36
(D) 54
(E) 90

As I don't have an OA this is how I arrived at (C) i.e. 36 as an answer. Can someone please let me know whether I am correct or not?

Total cost of 6 pounds of Maine Lobster = d ------------------------(1)
Total vats created = 6v--------------------------------------------(2)
Total bowls created = 6 bv ----------------------------------------(3)
Therefore cost of 6bv will be d dollars where b and v are two different prime numbers.

Prime factors of 36 are \(2^3 * 3^2\) i.e. 6 *2 *3 = 36

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Re: Lobsters  [#permalink]

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New post 27 Jan 2012, 14:52
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enigma123 wrote:
A restaurant pays a seafood distributor d dollars for 6 pounds of Maine lobster. Each pound can make v vats of lobster bisque, and each vat makes b bowls of lobster bisque. If the cost of the lobster per bowl is an integer, and if v and b are different prime integers, then which of the following is the smallest possible value of d?
(A) 15
(B) 24
(C) 36
(D) 54
(E) 90


d dollars = 6 pounds = 6v vats = 6vb bowls --> cost per bowl = d/(6vb). As given that d/(6vb) is an integer and v and b are different primes, then d/(6vb)=d/(6*2*3)=d/36=integer (d min is for min values of v and b, so for 2 and 3). Hence min value of d is 36.

Answer: C.
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Re: A restaurant pays a seafood distributor d dollars for 6  [#permalink]

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New post 27 Jan 2012, 16:42
What if the "cost of the bowl is an integer" is not given? I mean how does it change the answer?
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Re: A restaurant pays a seafood distributor d dollars for 6  [#permalink]

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New post 27 Jan 2012, 17:38
docabuzar wrote:
What if the "cost of the bowl is an integer" is not given? I mean how does it change the answer?


If we assume that d is some real amount in cents, then min value of d will be be $0.01 (1 cent). Though in this case the whole question wouldn't make much sense.
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Re: A restaurant pays a seafood distributor d dollars for 6  [#permalink]

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New post 27 Dec 2016, 03:10
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Let’s start by finding the cost of the lobster, per bowl, in terms of the variables given (d, v, and b).

(d dollars/6 pounds) x (1 pound/v vats) x (1 vat/b bowls) = (d/6vb)

The problem states that this value, the cost of the lobster per bowl, or (d/6vb), is an integer. In other words, d is divisible by 6vb. To make d as small as possible, we need to make 6vb as small as possible. Since v and b are different prime integers, the smallest value of 6vb is 36 (using the two smallest prime integers, v = 2 and b = 3, or v = 3 and b = 2).

In order to make the cost of the lobster per bowl an integer, d must be divisible by 36. In other words, d must be a multiple of 36. What’s the smallest possible multiple of 36? The smallest multiple of 36 is 36.

The correct answer is C, 36.
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Re: A restaurant pays a seafood distributor d dollars for 6  [#permalink]

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New post 23 Aug 2018, 16:51
enigma123 wrote:
A restaurant pays a seafood distributor d dollars for 6 pounds of Maine lobster. Each pound can make v vats of lobster bisque, and each vat makes b bowls of lobster bisque. If the cost of the lobster per bowl is an integer, and if v and b are different prime integers, then which of the following is the smallest possible value of d?
(A) 15
(B) 24
(C) 36
(D) 54
(E) 90


Since we are looking for the smallest possible value of d, we can let v = 2 and b = 3. That is, a pound of lobster can make 2 vats of lobster bisque and each vat makes 3 bowls of lobster bisque. Therefore, a pound of lobster can make 6 bowls of lobster bisque. We can assume that the cost of each bowl of lobster bisque is $1. So 6 bowls = $6. In other words, a pound of lobster makes $6, so 6 pounds of lobster is (at least) $36.

Answer: C
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Re: A restaurant pays a seafood distributor d dollars for 6 &nbs [#permalink] 23 Aug 2018, 16:51
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